Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon

Area of Trapezium and a Polygon Exercise 20A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Find the area of a triangle, whose sides are :
(i) 10 cm, 24 cm and 26 cm
(ii) 18 mm, 24 mm and 30 mm
(iii) 21 m, 28 m and 35 m
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20A 1
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20A 2
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20A 3

Question 2.
Two sides of a triangle are 6 cm and 8 cm. If height of the triangle corresponding to 6 cm side is 4 cm ; find :
(i) area of the triangle
(ii) height of the triangle corresponding to 8 cm side.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20A 4

Question 3.
The sides of a triangle are 16 cm, 12 cm and 20 cm. Find :
(i) area of the triangle ;
(ii) height of the triangle, corresponding to the largest side ;
(iii) height of the triangle, corresponding to the smallest side.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20A 5
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20A 6

Question 4.
Two sides of a triangle are 6.4 m and 4.8 m. If height of the triangle corresponding to 4.8 m side is 6 m; find :
(i) area of the triangle ;
(ii) height of the triangle corresponding to 6.4 m side.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20A 7

Question 5.
The base and the height of a triangle are in the ratio 4 : 5. If the area of the triangle is 40 m2; find its base and height.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20A 8

Question 6.
The base and the height of a triangle are in the ratio 5 : 3. If the area of the triangle is 67.5 m2; find its base and height.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20A 9

Question 7.
The area of an equilateral triangle is 144√3 cm2; find its perimeter.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20A 10

Question 8.
The area of an equilateral triangle is numerically equal to its perimeter. Find its perimeter correct to 2 decimal places.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20A 11

Question 9.
A field is in the shape of a quadrilateral ABCD in which side AB = 18 m, side AD = 24 m, side BC = 40m, DC = 50 m and angle A = 90°. Find the area of the field.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20A 12

Question 10.
The lengths of the sides of a triangle are in the ratio 4 : 5 : 3 and its perimeter is 96 cm. Find its area.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20A 13
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20A 14

Question 11.
One of the equal sides of an isosceles triangle is 13 cm and its perimeter is 50 cm. Find the area of the triangle.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20A 15

Question 12.
The altitude and the base of a triangular field are in the ratio 6 : 5. If its cost is ₹ 49,57,200 at the rate of ₹ 36,720 per hectare and 1 hectare = 10,000 sq. m, find (in metre) dimensions of the field,
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20A 16

Question 13.
Find the area of the right-angled triangle with hypotenuse 40 cm and one of the other two sides 24 cm.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20A 17

Question 14.
Use the information given in the adjoining figure to find :
(i) the length of AC.
(ii) the area of a ∆ABC
(iii) the length of BD, correct to one decimal place.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20A Q14
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20A 18

Area of Trapezium and a Polygon Exercise 20B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Find the length and perimeter of a rectangle, whose area = 120 cm2 and breadth = 8 cm
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20B 19

Question 2.
The perimeter of a rectangle is 46 m and its length is 15 m. Find its :
(i) breadth
(ii) area
(iii) diagonal.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20B 20

Question 3.
The diagonal of a rectangle is 34 cm. If its breadth is 16 cm; find its :
(i) length
(ii) area
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20B 21

Question 4.
The area of a small rectangular plot is 84 m2. If the difference between its length and the breadth is 5 m; find its perimeter.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20B 22

Question 5.
The perimeter of a square is 36 cm; find its area
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20B 23

Question 6.
Find the perimeter of a square; whose area is : 1.69 m2
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20B 24

Question 7.
The diagonal of a square is 12 cm long; find its area and length of one side.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20B 25

Question 8.
The diagonal of a square is 15 m; find the length of its one side and perimeter.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20B 26

Question 9.
The area of a square is 169 cm2. Find its:
(i) one side
(ii) perimeter
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20B 27

Question 10.
The length of a rectangle is 16 cm and its perimeter is equal to the perimeter of a square with side 12.5 cm. Find the area of the rectangle.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20B 28

Question 11.
The perimeter of a square is numerically equal to its area. Find its area.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20B 29

Question 12.
Each side of a rectangle is doubled. Find the ratio between :
(i) perimeters of the original rectangle and the resulting rectangle.
(ii) areas of the original rectangle and the resulting rectangle.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20B 30

Question 13.
In each of the following cases ABCD is a square and PQRS is a rectangle. Find, in each case, the area of the shaded portion.
(All measurements are in metre).
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20B Q13
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20B 31

Question 14.
A path of uniform width, 3 m, runs around the outside of a square field of side 21 m. Find the area of the path.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20B 32

Question 15.
A path of uniform width, 2.5 m, runs around the inside of a rectangular field 30 m by 27 m. Find the area of the path.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20B 33

Question 16.
The length of a hall is 18 m and its width is 13.5 m. Find the least number of square tiles, each of side 25 cm, required to cover the floor of the hall,
(i) without leaving any margin.
(ii) leaving a margin of width 1.5 m all around. In each case, find the cost of the tiles required at the rate of Rs. 6 per tile
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20B 34
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20B 35

Question 17.
A rectangular field is 30 m in length and 22m in width. Two mutually perpendicular roads, each 2.5 m wide, are drawn inside the field so that one road is parallel to the length of the field and the other road is parallel to its width. Calculate the area of the crossroads.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20B 36

Question 18.
The length and the breadth of a rectangular field are in the ratio 5 : 4 and its area is 3380 m2. Find the cost of fencing it at the rate of ₹75 per m.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20B 37

Question 19.
The length and the breadth of a conference hall are in the ratio 7 : 4 and its perimeter is 110 m. Find:
(i) area of the floor of the hall.
(ii) number of tiles, each a rectangle of size 25 cm x 20 cm, required for flooring of the hall.
(iii) the cost of the tiles at the rate of ₹ 1,400 per hundred tiles.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20B 38
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20B 39

Area of Trapezium and a Polygon Exercise 20C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
The following figure shows the cross-section ABCD of a swimming pool which is trapezium in shape.
If the width DC, of the swimming pool is 6.4cm, depth (AD) at the shallow end is 80 cm and depth (BC) at deepest end is 2.4m, find Its area of the cross-section.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20C Q1
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20C 40

Question 2.
The parallel sides of a trapezium are in the ratio 3 : 4. If the distance between the parallel sides is 9 dm and its area is 126 dm2 ; find the lengths of its parallel sides.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20C 41

Question 3.
The two parallel sides and the distance between them are in the ratio 3 : 4 : 2. If the area of the trapezium is 175 cm2, find its height.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20C 42

Question 4.
A parallelogram has sides of 15 cm and 12 cm; if the distance between the 15 cm sides is 6 cm; find the distance between 12 cm sides.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20C 43

Question 5.
A parallelogram has sides of 20 cm and 30 cm. If the distance between its shorter sides is 15 cm; find the distance between the longer sides.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20C 44

Question 6.
The adjacent sides of a parallelogram are 21 cm and 28 cm. If its one diagonal is 35 cm; find the area of the parallelogram.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20C 45
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20C 46

Question 7.
The diagonals of a rhombus are 18 cm and 24 cm. Find:
(i) its area ;
(ii) length of its sides.
(iii) its perimeter;
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20C 47
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20C 48

Question 8.
The perimeter of a rhombus is 40 cm. If one diagonal is 16 cm; find :
(i) its another diagonal
(ii) area
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20C 49
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20C 50

Question 9.
Each side of a rhombus is 18 cm. If the distance between two parallel sides is 12 cm, find its area.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20C 51

Question 10.
The length of the diagonals of a rhombus is in the ratio 4 : 3. If its area is 384 cm2, find its side.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20C 52

Question 11.
A thin metal iron-sheet is rhombus in shape, with each side 10 m. If one of its diagonals is 16 m, find the cost of painting its both sides at the rate of ₹ 6 per m2.
Also, find the distance between the opposite sides of this rhombus.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20C 53
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20C 54

Question 12.
The area of a trapezium is 279 sq.cm and the distance between its two parallel sides is 18 cm. If one of its parallel sides is longer than the other side by 5 cm, find the lengths of its parallel sides.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20C 55

Question 13.
The area of a rhombus is equal to the area of a triangle. If base of ∆ is 24 cm, its corresponding altitude is 16 cm and one of the diagonals of the rhombus is 19.2 cm. Find its other diagonal.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20C 56

Question 14.
Find the area of the trapezium ABCD in which AB//DC, AB = 18 cm, ∠B = ∠C = 90°, CD = 12 cm and AD = 10 cm.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20C 57

Area of Trapezium and a Polygon Exercise 20D – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Find the radius and area of a circle, whose circumference is :
(i) 132 cm
(ii) 22 m
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20D 58

Question 2.
Find the radius and circumference of a circle, whose area is :
(i) 154 cm2
(ii) 6.16 m2
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20D 59
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20D 60

Question 3.
The circumference of a circular table is 88 m. Find its area.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20D 61

Question 4.
The area of a circle is 1386 sq.cm ; find its circumference.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20D 62

Question 5.
Find the area of a flat circular ring formed by two concentric circles (circles with same centre) whose radii are 9 cm and 5 cm.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20D 63

Question 6.
Find the area of the shaded portion in each of the following diagrams :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20D Q6
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20D 64
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20D 65

Question 7.
The radii of the inner and outer circumferences of a circular running track are 63 m and 70 m respectively. Find :
(i) the area of the track ;
(it) the difference between the lengths of the two circumferences of the track.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20D 66
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20D 67

Question 8.
A circular field cf radius 105 m has a circular path of uniform width of 5 m along and inside its boundary. Find the area of the path.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20D 68

Question 9.
There is a path of uniform width 7 m round and outside a circular garden of diameter 210 m. Find the area of the path.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20D 69

Question 10.
A wire, when bent in the form of a square encloses an area of 484 cm2. Find :
(i) one side of the square ;
(ii) length of the wire ;
(iii) the largest area enclosed; if the same wire is bent to form a circle.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20D 70

Question 11.
A wire, when bent in the form of a square; encloses an area of 196 cm2. If the same wire is bent to form a circle; find the area of the circle.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20D 71

Question 12.
The radius of a circular wheel is 42 cm. Find the distance travelled by it in :
(i) 1 revolution ;
(ii) 50 revolutions ;
(iii) 200 revolutions ;
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20D 72

Question 13.
The diameter of a wheel is 0.70 m. Find the distance covered by it in 500 revolutions. If the wheel takes 5 minutes to make 500 revolutions; find its speed in :
(i) m/s
(ii) km/hr.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20D 73

Question 14.
A bicycle wheel, diameter 56 cm, is making 45 revolutions in every 10 seconds. At what speed in kilometre per hour is the bicycle travelling ?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20D 74

Question 15.
A roller has a diameter of 1.4 m. Find :
(i) its circumference ;
(ii) the number of revolutions it makes while travelling 61.6 m.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20D 75

Question 16.
Find the area of the circle, length of whose circumference is equal to the sum of the lengths of the circumferences with radii 15 cm and 13 cm.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20D 76

Question 17.
A piece of wire of length 108 cm is bent to form a semicircular arc bounded by its diameter. Find its radius and area enclosed.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20D 77

Question 18.
In the following figure, a rectangle ABCD enclosed three circles. If BC = 14 cm, find the area of the shaded portion (Take π = 22/7)
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20D Q18
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 20 Area of Trapezium and a Polygon Ex 20D 78

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 19 Representing 3-D in 2-D

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 19 Representing 3-D in 2-D

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 19 Representing 3-D in 2-D

Representing 3-D in 2-D Exercise 19 – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
If a polyhedron has 8 faces and 8 vertices, find the number of edges in it.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 19 Representing 3-D in 2-D 1

Question 2.
If a polyhedron has 10 vertices and 7 faces, find the number of edges in it.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 19 Representing 3-D in 2-D 2

Question 3.
State, the number of faces, number of vertices and number of edges of:
(i) a pentagonal pyramid
(ii) a hexagonal prism
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 19 Representing 3-D in 2-D 3

Question 4.
Verily Euler’s formula for the following three dimensional figures:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 19 Representing 3-D in 2-D Q4
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 19 Representing 3-D in 2-D 4

Question 5.
Can a polyhedron have 8 faces, 26 edges and 16 vertices?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 19 Representing 3-D in 2-D 5

Question 6.
Can a polyhedron have:
(i) 3 triangles only ?
(ii) 4 triangles only ?
(iii) a square and four triangles ?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 19 Representing 3-D in 2-D 6

Question 7.
Using Euler’s formula, find the values of x, y, z.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 19 Representing 3-D in 2-D Q7
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 19 Representing 3-D in 2-D 7

Question 8.
What is the least number of planes that can enclose a solid? What is the name of the solid.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 19 Representing 3-D in 2-D 8

Question 9.
Is a square prism same as a cube?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 19 Representing 3-D in 2-D 9

Question 10.
A cubical box is 6 cm x 4 cm x 2 cm. Draw two different nets of it.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 19 Representing 3-D in 2-D 10

Question 11.
Dice are cubes where the sum of the numbers on the opposite faces is 7. Find the missing numbers a, b and c.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 19 Representing 3-D in 2-D Q11
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 19 Representing 3-D in 2-D 11

Question 12.
Name the polyhedron that can be made by folding each of the following nets:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 19 Representing 3-D in 2-D Q12
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 19 Representing 3-D in 2-D 12

Question 13.
Draw nets for the following polyhedrons:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 19 Representing 3-D in 2-D Q13
Solution:
<Selina Concise Mathematics Class 8 ICSE Solutions Chapter 19 Representing 3-D in 2-D 13

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only)

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only)

Constructions Exercise 18A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Given below are the angles x and y.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A Q1
Without measuring these angles, construct :
(i) ∠ABC = x + y
(ii) ∠ABC = 2x + y
(iii) ∠ABC = x + 2y
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A 1
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A 2
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A 3

Question 2.
Given below are the angles x, y and z.
Without measuring these angles construct :
(i) ∠ABC = x + y + z
(ii) ∠ABC = 2x + y + z
(iii) ∠ABC = x + 2y + z
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A Q2
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A 4
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A 5
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A 6

Question 3.
Draw a line segment BC = 4 cm. Construct angle ABC = 60°.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A 7

Question 4.
Construct angle ABC = 45° in which BC = 5 cm and AB = 4.6 cm.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A 8

Question 5.
Construct angle ABC = 90°. Draw BP, the bisector of angle ABC. State the measure of angle PBC.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A 9

Question 6.
6. Draw angle ABC of any suitable measure.
(i) Draw BP, the bisector of angle ABC.
(ii) Draw BR, the bisector of angle PBC and draw BQ, the bisector of angle ABP.
(iii) Are the angles ABQ, QBP, PBR and RBC equal?
(iv) Are the angles ABR and QBC equal ?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A 10

Constructions Exercise 18B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Draw a line segment AB of length 5.3 cm. Using two different methods bisect AB.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18B 11
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18B 12

Question 2.
Draw a line segment PQ = 4.8 cm. Construct the perpendicular bisector of PQ.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18B 13

Question 3.
In each of the following, draw perpendicular through point P to the line segment AB :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18B Q3
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18B 14
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18B 15
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18B 16

Question 4.
Draw a line segment AB = 5.5 cm. Mark a point P, such that PA = 6 cm and PB = 4.8 cm. From the point P, draw a perpendicular to AB.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18B 17

Question 5.
Draw a line segment AB = 6.2 cm. Mark a point P in AB such that BP = 4 cm. Through point P draw perpendicular to AB.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18B 18

Constructions Exercise 18C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Draw a line AB = 6 cm. Mark a point P any where outside the line AB. Through the point P, construct a line parallel to AB.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18C 19

Question 2.
Draw a line MN = 5.8 cm. Locate a point A which is 4.5 cm from M and 5 cm from N. Through A draw a line parallel to line MN.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18C 20

Question 3.
Draw a straight line AB = 6.5 cm. Draw another line which is parallel to AB at a distance of 2.8 cm from it.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18C 21

Question 4.
Construct an angle PQR = 80°. Draw a line parallel to PQ at a distance of 3 cm from it and another line parallel to QR at a distance of 3.5 cm from it. Mark the point of intersection of these parallel lines as A.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18C 22

Question 5.
Draw an angle ABC = 60°. Draw the bisector of it. Also draw a line parallel to BC a distance of 2.5 cm from it.
Let this parallel line meet AB at point P and angle bisector at point Q. Measure the length of BP and PQ. Is BP = PQ?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18C 23

Question 6.
Construct an angle ABC = 90°. Locate a point P which is 2.5 cm from AB and 3.2 cm from BC.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18C 24

Constructions Exercise 18D – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Construct a quadrilateral ABCD; if:
(i) AB = 4.3 cm, BC = 5.4, CD = 5 cm, DA = 4.8 cm and angle ABC = 75°.
(ii) AB = 6 cm, CD = 4.5 cm, BC = AD = 5 cm and ∠BCD = 60°.
(iii) AB = 8 cm, BC = 5.4 cm, AD = 6 cm, ∠A = 60° and ∠B = 75°.
(iv) AB = 5 cm, BC = 6.5 cm, CD =4.8 cm, ∠B = 75° and ∠C = 120°.
(v) AB = 6 cm = AC, BC = 4 cm, CD = 5 cm and AD = 4.5 cm.
(vi) AB = AD = 5cm, BD = 7 cm and BC = DC = 5.5 cm
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 25
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 26
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 27
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 28
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 29
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 30
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 31
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 32

Question 2.
Construct a parallelogram ABCD, if :
(i) AB = 3.6 cm, BC = 4.5 cm and ∠ABC = 120°.
(ii) BC = 4.5 cm, CD = 5.2 cm and ∠ADC = 75°.
(iii) AD = 4 cm, DC = 5 cm and diagonal BD = 7 cm.
(iv) AB = 5.8 cm, AD = 4.6 cm and diagonal AC = 7.5 cm.
(v) diagonal AC = 6.4 cm, diagonal BD = 5.6 cm and angle between the diagonals is 75°.
(vi) lengths of diagonals AC and BD are 6.3 cm and 7.0 cm respectively, and the angle between them is 45°.
(vii) lengths of diagonals AC and BD are 5.4 cm and 6.7 cm respectively and the angle between them is 60°.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 33
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 34
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 35
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 36
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 37
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 38
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 39
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 40
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 41

Question 3.
Construct a rectangle ABCD ; if :
(i) AB = 4.5 cm and BC = 5.5 cm.
(ii) BC = 61 cm and CD = 6.8 cm.
(iii) AB = 5.0 cm and diagonal AC = 6.7 cm.
(iv) AD = 4.8 cm and diagonal AC = 6.4 cm.
(v) each diagonal is 6 cm and the angle between them is 45°.
(vi) each diagonal is 5.5 cm and the angle between them is 60°.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 42
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 43
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 44
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 45
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 46
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 47

Question 4.
Construct a rhombus ABCD, if ;
(i) AB = 4 cm and ∠B = 120°.
(ii) BC = 4.7 cm and ∠B = 75°.
(iii) CD = 5 cm and diagonal BD = 8.5 cm.
(iv) BC = 4.8cm, and diagonal AC = 7cm.
(v) diagonal AC = 6 cm and diagonal BD = 5.8 cm.
(vi) diagonal AC = 4.9 cm and diagonal BD = 6 cm.
(vii) diagonal AC = 6.6 cm and diagonal BD = 5.3 cm.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 48
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 49
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 50
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 51
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 52
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 53
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 54

Question 5.
Construct a square, if :
(i) its one side is 3.8 cm.
(ii) its each side is 4.3 cm.
(iii) one diagonal is 6.2 cm.
(iv) each diagonal is 5.7 cm.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 55
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 56
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 57
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 58

Question 6.
Construct a quadrilateral ABCD in which ; ∠A = 120°, ∠B = 60°, AB = 4 cm, BC = 4.5 cm and CD = 5 cm.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 59
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 60

Question 7.
Construct a quadrilateral ABCD, such that AB = BC = CD = 4.4 cm, ∠B = 90° and ∠C = 120°.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 61
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 62

Question 8.
Using ruler and compasses only, construct a parallelogram ABCD, in which : AB = 6 cm, AD = 3 cm and ∠DAB = 60°. In the same figure draw the bisector of angle DAB and let it meet DC at point P. Measure angle APB.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 63

Question 9.
Draw a parallelogram ABCD, with AB = 6 cm, AD = 4.8 cm and ∠DAB = 45°. Draw the perpendicular bisector of side AD and let it meet AD at point P. Also draw the diagonals AC and BD ; and let they intersect at point O. Join O and P. Measure OP.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 64

Question 10.
Using ruler and compasses only, construct a rhombus whose diagonals are 8 cm and 6 cm. Measure the length of its one side.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 65

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals

Special Types of Quadrilaterals Exercise 17 – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
In parallelogram ABCD, ∠A = 3 times ∠B. Find all the angles of the parallelogram. In the same parallelogram, if AB = 5x – 7 and CD = 3x +1 ; find the length of CD.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 1
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 2

Question 2.
In parallelogram PQRS, ∠Q = (4x – 5)° and ∠S = (3x + 10)°. Calculate : ∠Q and ∠R.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 3

Question 3.
In rhombus ABCD ;
(i) if ∠A = 74° ; find ∠B and ∠C.
(ii) if AD = 7.5 cm ; find BC and CD.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 4

Question 4.
In square PQRS :
(i) if PQ = 3x – 7 and QR = x + 3 ; find PS
(ii) if PR = 5x and QR = 9x – 8. Find QS
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 5
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 6

Question 5.
ABCD is a rectangle, if ∠BPC = 124°
Calculate : (i) ∠BAP (ii) ∠ADP
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals Q5
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 7

Question 6.
ABCD is a rhombus. If ∠BAC = 38°, find :
(i) ∠ACB
(ii) ∠DAC
(iii) ∠ADC.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals Q6
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 8

Question 7.
ABCD is a rhombus. If ∠BCA = 35°. find ∠ADC.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 9

Question 8.
PQRS is a parallelogram whose diagonals intersect at M.
If ∠PMS = 54°, ∠QSR = 25° and ∠SQR = 30° ; find :
(i) ∠RPS
(ii) ∠PRS
(iii) ∠PSR.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 10

Question 9.
Given : Parallelogram ABCD in which diagonals AC and BD intersect at M.
Prove : M is mid-point of LN.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 11

Question 10.
In an Isosceles-trapezium, show that the opposite angles are supplementary.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 12

Question 11.
ABCD is a parallelogram. What kind of quadrilateral is it if :
(i) AC = BD and AC is perpendicular to BD?
(ii) AC is perpendicular to BD but is not equal to it?
(iii) AC = BD but AC is not perpendicular to BD?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 13
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 14

Question 12.
Prove that the diagonals of a parallelogram bisect each other.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 15

Question 13.
If the diagonals of a parallelogram are of equal lengths, the parallelogram is a rectangle. Prove it.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 16

Question 14.
In parallelogram ABCD, E is the mid-point of AD and F is the mid-point of BC. Prove that BFDE is a parallelogram.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 17

Question 15.
In parallelogram ABCD, E is the mid-point of side AB and CE bisects angle BCD. Prove that :
(i) AE = AD,
(ii) DE bisects and ∠ADC and
(iii) Angle DEC is a right angle.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 18
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 19

Question 16.
In the following diagram, the bisectors of interior angles of the parallelogram PQRS enclose a quadrilateral ABCD.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals Q16
Show that:
(i) ∠PSB + ∠SPB = 90°
(ii) ∠PBS = 90°
(iii) ∠ABC = 90°
(iv) ∠ADC = 90°
(v) ∠A = 90°
(vi) ABCD is a rectangle
Thus, the bisectors of the angles of a parallelogram enclose a rectangle.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 20
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 21

Question 17.
In parallelogram ABCD, X and Y are midpoints of opposite sides AB and DC respectively. Prove that:
(i) AX = YC
(ii) AX is parallel to YC
(iii) AXCY is a parallelogram.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 22

Question 18.
The given figure shows a parallelogram ABCD. Points M and N lie in diagonal BD such that DM = BN.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals Q18
Prove that:
(i) ∆DMC = ∆BNA and so CM = AN
(ii) ∆AMD = ∆CNB and so AM CN
(iii) ANCM is a parallelogram.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 23

Question 19.
The given figure shows a rhombus ABCD in which angle BCD = 80°. Find angles x and y.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals Q19
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 24

Question 20.
Use the information given in the alongside diagram to find the value of x, y and z.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals Q20
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 25

Question 21.
The following figure is a rectangle in which x : y = 3 : 7; find the values of x and y.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals Q21
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 26

Question 22.
In the given figure, AB || EC, AB = AC and AE bisects ∠DAC. Prove that:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals Q22
(i) ∠EAC = ∠ACB
(ii) ABCE is a parallelogram.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals 27

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability

Probability Exercise 23 – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
A die is thrown, find the probability of getting:
(i) a prime number
(ii) a number greater than 4
(iii) a number not greater than 4.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability 1
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability 2

Question 2.
A coin is tossed. What is the probability of getting:
(i) a tail? (ii) ahead?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability 3

Question 3.
A coin is tossed twice. Find the probability of getting:
(i) exactly one head (ii) exactly one tail
(iii) two tails (iv) two heads
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability 4
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability 5

Question 4.
A letter is chosen from the word ‘PENCIL’ what is the probability that the letter chosen is a consonant?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability 6

Question 5.
A bag contains a black ball, a red ball and a green ball, all the balls are identical in shape and size. A ball is drawn from the bag without looking into it. What is the probability that the ball drawn is:
(i) a red ball
(ii) not a red ball
(iii) a white ball.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability 7

Question 6.
6. In a single throw of a die, find the probability of getting a number
(i) greater than 2
(ii) less than or equal to 2
(iii) not greater than 2.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability 8

Question 7.
A bag contains 3 white, 5 black and 2 red balls, all of the same shape and size.
A ball is drawn from the bag without looking into it, find the probability that the ball drawn is:
(i) a black ball.
(ii) a red ball.
(iii) a white ball.
(iv) not a red ball.
(v) not a black ball.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability 9
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability 10

Question 8.
In a single throw of a die, find the probability that the number:
(i) will be an even number.
(ii) will be an odd number.
(iii) will not be an even number.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability 11

Question 9.
In a single throw of a die, find the probability of getting :
(i) 8
(ii) a number greater than 8
(iii) a number less than 8
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability 12

Question 10.
Which of the following can not be the probability of an event?
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability Q10
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability 13

Question 11.
A bag contains six identical black balls. A child withdraws one ball from the bag without looking into it. What is the probability that he takes out:
(i) a white ball,
(ii) a black ball
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability 14

Question 12.
Three identical coins are tossed together. What is the probability of obtaining:
all heads?
exactly two heads?
exactly one head?
no head?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability 15

Question 13.
A book contains 92 pages. A page is chosen at random. What is the probability that the sum of the digits in the page number is 9?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability 16

Question 14.
Two coins are tossed together. What is the probability of getting:
(i) at least one head
(ii) both heads or both tails.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability 17

Question 15.
From 10 identical cards, numbered 1, 2, 3, …… , 10, one card is drawn at random. Find the probability that the number on the card drawn is a multiple of:
(i) 2 (ii) 3
(iii) 2 and 3 (iv) 2 or 3
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability 18

Question 16.
Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is:
(i) 0
(ii) 12
(iii) less than 12
(iv) less than or equal to 12
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability 19

Question 17.
A die is thrown once. Find the probability of getting:
(i) a prime number
(ii) a number greater than 3
(iii) a number other than 3 and 5
(iv) a number less than 6
(v) a number greater than 6.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability 20

Question 18.
Two coins are tossed together. Find the probability of getting:
(i) exactly one tail
(ii) at least one head
(iii) no head
(iv) at most one head
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 23 Probability 21

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling

Data Handling Exercise 22A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Arrange the following data as an array (in ascending order):
(i) 7, 5, 15, 12, 10, 11, 16
(ii) 6.3, 5.9, 9.8, 12.3, 5.6, 4.7
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22A 1

Question 2.
Arrange the following data as an array (descending order):
(i) 0 2, 0, 3, 4, 1, 2, 3, 5
(ii) 9.1, 3.7, 5.6, 8.3, 11.5, 10.6
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22A 2

Question 3.
Construct a frequency table for the following data:
(i) 6, 7, 5, 6, 8, 9, 5, 5, 6, 7, 8, 9, 8, 10, 10, 9, 8, 10, 5, 7, 6, 8.
(ii) 3, 2, 1, 5, 4, 3, 2, 5, 5, 4, 2, 2, 2, 1, 4, 1, 5, 4.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22A 3

Question 4.
Following are the marks obtained by 30 students in an examinations.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22A Q4
Taking class intervals 0-10, 10-20, ……… 40-50 ; construct a frequency table.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22A 4

Question 5.
Construct a frequency distribution table for the following data ; taking class-intervals 4-6, 6-8, ……… 14-16.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22A Q5
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22A 5

Question 6.
Fill in the blanks:
(i) Lower class limit of 15-18 is ………
(ii) Upper class limit of 24-30 is ……..
(iii) Upper limit of 5-12.5 is ………
(iv) If the upper and the lower limits of a class interval are 16 and 10 ; the class-interval is ……..
(v) If the lower and the upper limits of a class interval are 7.5 and 12.5 ; the class interval is ……..
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22A 6

Data Handling Exercise 22B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Hundred students from a certain locality use different modes of travelling to school as given below. Draw a bar graph.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22B Q1
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22B 7

Question 2.
Mr. Mirza’s monthly income is Rs. 7,200. He spends Rs. 1,800 on rent, Rs. 2,700 on food, Rs. 900 on education of his children ; Rs. 1,200 on Other things and saves the rest.
Draw a pie-chart to represent it.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22B 8

Question 3.
The percentage of marks obtained, in different subjects by Ashok Sharma (in an examination) are given below. Draw a bar graph to represent it.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22B Q3
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22B 9

Question 4.
The following table shows the market position of different brand of tea-leaves.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22B Q4
Draw it-pie-chart to represent the above information.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22B 10

Question 5.
Students of a small school use different modes of travel to school as shown below:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22B Q5
Draw a suitable bar graph.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22B 11

Question 6.
For the following table, draw a bar-graph
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22B Q6
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22B 12

Question 7.
Manoj appeared for ICSE examination 2018 and secured percentage of marks as shown in the following table:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22B Q7
Represent the above data by drawing a suitable bar graph.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22B 13

Question 8.
For the data given above in question number 7, draw a suitable pie-graph.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22B 14

Question 9.
Mr. Kapoor compares the prices (in Rs.) of different items at two different shops A and B. Examine the following table carefully and represent the data by a double bar graph.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22B Q9
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22B 15

Question 10.
The following tables shows the mode of transport used by boys and girls for going to the same school.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22B Q10
Draw a double bar graph representing the above data.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 22 Data Handling Ex 22B 16

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder)

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder)

Surface Area, Volume and Capacity Exercise 21A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Find the volume and the total surface area of a cuboid, whose :
(i) length = 15 cm, breadth = 10 cm and height = 8 cm.
(ii) l = 3.5 m, b = 2.6 m and h = 90 cm,
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21A 1

Question 2.
(i) The volume of a cuboid is 3456 cm3. If its length = 24 cm and breadth = 18 cm ; find its height.
(ii) The volume of a cuboid is 7.68 m3. If its length = 3.2 m and height = 1.0 m; find its breadth.
(iii) The breadth and height of a rectangular solid are 1.20 m and 80 cm respectively. If the volume of the cuboid is 1.92 m3; find its length.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21A 2
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21A 3

Question 3.
The length, breadth and height of a cuboid are in the ratio 5 : 3 : 2. If its volume is 240 cm3; find its dimensions. (Dimensions means : its length, breadth and height). Also find the total surface area of the cuboid.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21A 4

Question 4.
The length, breadth and height of a cuboid are in the ratio 6 : 5 : 3. If its total surface area is 504 cm2; find its dimensions. Also, find the volume of the cuboid.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21A 5

Question 5.
Find the volume and total surface area of a cube whose each edge is :
(i) 8 cm
(ii) 2 m 40 cm.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21A 6

Question 6.
Find the length of each edge of a cube, if its volume is :
(i) 216 cm3
(ii) 1.728 m3
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21A 7

Question 7.
The total surface area of a cube is 216 cm2. Find its volume.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21A 8

Question 8.
A solid cuboid of metal has dimensions 24 cm, 18 cm and 4 cm. Find its volume.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21A 9

Question 9.
A wall 9 m long, 6 m high and 20 cm thick, is to be constructed using bricks of dimensions 30 cm, 15 cm and 10 cm. How many bricks will be required.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21A 10

Question 10.
A solid cube of edge 14 cm is melted down and recasted into smaller and equal cubes each of edge 2 cm; find the number of smaller cubes obtained.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21A 11

Question 11.
A closed box is cuboid in shape with length = 40 cm, breadth = 30 cm and height = 50 cm. It is made of thin metal sheet. Find the cost of metal sheet required to make 20 such boxes, if 1 m2 of metal sheet costs Rs. 45.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21A 12

Question 12.
Four cubes, each of edge 9 cm, are joined as shown below :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21A Q12
Write the dimensions of the resulting cuboid obtained. Also, find the total surface area and the volume of the resulting cuboid.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21A 13

Surface Area, Volume and Capacity Exercise 21B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
How many persons can be accommodated in a big-hall of dimensions 40 m, 25 m and 15 m ; assuming that each person requires 5 m3 of air?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21B 14

Question 2.
The dimension of a class-room are; length = 15 m, breadth = 12 m and height = 7.5 m. Find, how many children can be accommodated in this class-room ; assuming 3.6 m3 of air is needed for each child.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21B 15

Question 3.
The length, breadth and height of a room are 6 m, 5.4 m and 4 m respectively. Find the area of :
(i) its four-walls
(ii) its roof.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21B 16

Question 4.
A room 5 m long, 4.5 m wide and 3.6 m high has one door 1.5 m by 2.4 m and two windows, each 1 m by 0.75 m. Find :
(i) the area of its walls, excluding door and windows ;
(ii) the cost of distempering its walls at the rate of Rs.4.50 per m2.
(iii) the cost of painting its roof at the rate of Rs.9 per m2.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21B 17
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21B 18

Question 5.
The dining-hall of a hotel is 75 m long ; 60 m broad and 16 m high. It has five – doors 4 m by 3 m each and four windows 3 m by 1.6 m each. Find the cost of :
(i) papering its walls at the rate of Rs.12 per m2;
(ii) carpetting its floor at the rate of Rs.25 per m2.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21B 19

Question 6.
Find the volume of wood required to make a closed box of external dimensions 80 cm, 75 cm and 60 cm, the thickness of walls of the box being 2 cm throughout.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21B 20

Question 7.
A closed box measures 66 cm, 36 cm and 21 cm from outside. If its walls are made of metal-sheet, 0.5 cm thick ; find :
(i) the capacity of the box ;
(ii) volume of metal-sheet and
(iii) weight of the box, if 1 cm3 of metal weights 3.6 gm.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21B 21

Question 8.
The internal length, breadth and height of a closed box are 1 m, 80 cm and 25 cm. respectively. If its sides are made of 2.5 cm thick wood ; find :
(i) the capacity of the box
(ii) the volume of wood used to make the box.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21B 22

Question 9.
Find the area of metal-sheet required to make an open tank of length = 10 m, breadth = 7.5 m and depth = 3.8 m.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21B 23

Question 10.
A tank 30 m long, 24 m wide and 4.5 m deep is to be made. It is open from the top. Find the cost of iron-sheet required, at the rate of ₹ 65 per m2, to make the tank.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21B 24

Surface Area, Volume and Capacity Exercise 21C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
The edges of three solid cubes are 6 cm, 8 cm and 10 cm. These cubes are melted and recast into a single cube. Find the edge of the resulting cube.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21C 25

Question 2.
Three solid cubes of edges 6 cm, 10 cm and x cm are melted to form a single cube of edge 12 cm, find the value of x.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21C 26

Question 3.
The length of the diagonals of a cube is 8√3 cm.
Find its:
(i) edge
(ii) total surface area
(iii) Volume
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21C 27

Question 4.
A cube of edge 6 cm and a cuboid with dimensions 4 cm x x cm x 15 cm are equal in volume. Find:
(i) the value of x.
(ii) total surface area of the cuboid.
(iii) total surface area of the cube.
(iv) which of these two has greater surface and by how much?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21C 28

Question 5.
The capacity of a rectangular tank is 5.2 m3 and the area of its base is 2.6 x 104 cm2; find its height (depth).
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21C 29

Question 6.
The height of a rectangular solid is 5 times its width and its length is 8 times its height. If the volume of the wall is 102.4 cm3, find its length.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21C 30

Question 7.
The ratio between the lengths of the edges of two cubes are in the ratio 3 : 2. Find the ratio between their:
(i) total surface area
(ii) volume.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21C 31

Question 8.
The length, breadth and height of a cuboid (rectangular solid) are 4 : 3 : 2.
(i) If its surface are is 2548 cm2, find its volume.
(ii) If its volume is 3000 m3, find its surface area.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21C 32
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21C 33

Surface Area, Volume and Capacity Exercise 21D – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
The height of a circular cylinder is 20 cm and the diameter of its base is 14 cm. Find:
(i) the volume
(ii) the total surface area.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21D 34

Question 2.
Find the curved surface area and the total surface area of a right circular cylinder whose height is 15 cm and the diameter of the cross-section is 14 cm.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21D 35

Question 3.
Find the height of the cylinder whose radius is 7 cm and the total surface area is 1100 cm2.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21D 36

Question 4.
The curved surface area of a cylinder of height 14 cm is 88 cm2. Find the diameter of the base of the cylinder.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21D 37

Question 5.
The ratio between the curved surface area and the total surface area of a cylinder is 1 : 2. Find the ratio between the height and the radius of the cylinder.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21D 38

Question 6.
Find the capacity of a cylindrical container with internal diameter 28 cm and height 20 cm.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21D 39

Question 7.
The total surface area of a cylinder is 6512 cm2 and the circumference of its bases is 88 cm. Find:
(i) its radius
(ii) its volume
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21D 40

Question 8.
The sum of the radius and the height of a cylinder is 37 cm and the total surface area of the cylinder is 1628 cm2. Find the height and the volume of the cylinder.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21D 41

Question 9.
A cylindrical pillar has radius 21 cm and height 4 m. Find :
(i) the curved surface area of the pillar
(ii) cost of polishing 36 such cylindrical pillars at the rate of ₹ 12 per m2.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21D 42

Question 10.
If radii of two cylinders are in the ratio 4 : 3 and their heights are in the ratio 5 : 6, find the ratio of their curved surfaces.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21D 43

Surface Area, Volume and Capacity Exercise 21E – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
A cuboid is 8 m long, 12 m broad and 3.5 high, Find its
(i) total surface area
(ii) lateral surface area
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21E 44

Question 2.
How many bricks will be required for constructing a wall which is 16 m long, 3 m high and 22.5 cm thick, if each brick measures 25 cm x 11.25 cm x 6 cm?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21E 45

Question 3.
The length, breadth and height of cuboid are in the ratio 6 : 5 : 3. If its total surface area is 504 cm2, find its volume.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21E 46

Question 4.
The external dimensions of an open wooden box are 65 cm, 34 cm and 25 cm. If the box is made up of wood 2 cm thick, find the capacity of the box and the volume of wood used to make it.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21E 47

Question 5.
The curved surface area and the volume of a toy, cylindrical in shape, are 132 cm2 and 462 cm3 respectively. Find, its diameter and its length.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21E 48
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21E 49

Question 6.
The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of ₹ 10 per m2 is ₹ 15,000, find the height of the hall.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21E 50

Question 7.
The length of a hall is double its breadth. Its height is 3 m. The area of its four walls (including doors and windows) is 108 m2, find its volume.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21E 51

Question 8.
A solid cube of side 12 cm is cut into 8 identical cubes. What will be the side of the new cube? Also, find the ratio between the surface area of the original cube and the total surface area of all the small cubes formed.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21E 52
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21E 53

Question 9.
The diameter of a garden roller is 1.4 m and it 2 m long. Find the maximum area covered by it 50 revolutions?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21E 54

Question 10.
In a building, there are 24 cylindrical pillars. For each pillar, radius is 28 m and height is 4 m. Find the total cost of painting the curved surface area of the pillars at the rate of ₹ 8 per m2.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 21 Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) Ex 21E 55

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions)

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions)

Algebraic Expressions Exercise 11A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Separate the constants and variables from the following :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11A Q1
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11A 1

Question 2.
Write the number of terms in each of the following polynomials.
(i) 5x2 + 3 x ax
(ii) ax ÷ 4 – 7
(iii) ax – by + y x z
(iv) 23 + a x b ÷ 2.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11A 2

Question 3.
Separate monomials, binomials, trinomials and polynomials from the following algebraic expressions :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11A Q3
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11A 3

Question 4.
Write the degree of each polynomial given below :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11A Q4
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11A 4

Question 5.
Write the coefficient of :
(i) ab in 7abx ,
(ii) 7a in 7abx ;
(iii) 5x2 in 5x2 – 5x ;
(iv) 8 in a2 – 8ax + a ;
(v) 4xy in x2 – 4xy + y2.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11A 5

Question 6.
In \(\frac { 5 }{ 7 }\) xy2z3, write the coefficient of
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11A Q6
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11A 6

Question 7.
In each polynomial, given below, separate the like terms :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11A Q7
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11A 7

Algebraic Expressions Exercise 11B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Evaluate :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11B Q1
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11B 8

Question 2.
Add :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11B Q2
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11B 9
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11B 10

Question 3.
Find the total savings of a boy who saves ₹ (4x – 6y) ; ₹ (6x + 2y) ; ₹ (4y – x) and ₹ (y – 2x) for four consecutive weeks.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11B 11

Question 4.
Subtract :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11B Q4
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11B 12
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11B 13

Question 5.
(i) Take away – 3x3 + 4x2 – 5x + 6 from 3x3 – 4x2 + 5x – 6
(ii) Take m2 + m + 4 from -m2 + 3m + 6 and the result from m2 + m + 1.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11B 14

Question 6.
Subtract the sum of 5y2 + y – 3 and y2 – 3y + 7 from 6y2 + y – 2.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11B 15

Question 7.
What must be added to x4 – x3 + x2 + x + 3 to obtain x4 + x2 – 1 ?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11B 16

Question 8.
(i) How much more than 2x2 + 4xy + 2y2 is 5x2 + 10xy – y2 ?
(ii) How much less 2a2 + 1 is than 3a2 – 6 ?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11B 17

Question 9.
If x = 6a + 86 + 9c ; y = 2b – 3a – 6c and z = c – b + 3a ; find
(i) x + y + z
(ii) x – y + z
(iii) 2x – y – 3z
(iv) 3y – 2z – 5x
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11B 18

Question 10.
The sides of a triangle are x2 – 3xy + 8, 4x2 + 5xy – 3 and 6 – 3x2 + 4xy. Find its perimeter.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11B 19

Question 11.
The perimeter of a triangle is 8y2 – 9y + 4 and its two sides are 3y2 – 5y and 4y2 + 12. Find its third side.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11B 20

Question 12.
The two adjacent sides of a rectangle are 2x2 – 5xy + 3z2 and 4xy – x2 – z2. Find its perimeter.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11B 21

Question 13.
What must be subtracted from 19x4 + 2x3 + 30x – 37 to get 8x4 + 22x3 – 7x – 60 ?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11B 22

Question 14.
How much smaller is 15x – 18y + 19z than 22x – 20y – 13z + 26 ?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11B 23

Question 15.
How much bigger is 15x2y2 – 18xy2 – 10x2y than -5x2 + 6x2y – 7xy ?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11B 24

Algebraic Expressions Exercise 11C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Multiply :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11C Q1
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11C 25
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11C 26
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11C 27
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11C 28

Question 2.
Multiply :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11C Q2
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11C 29
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11C 30

Question 3.
Simplify :
(i) (7x – 8) (3x + 2)
(ii) (px – q) (px + q)
(iii) (5a + 5b – c) (2b – 3c)
(iv) (4x – 5y) (5x – 4y)
(v) (3y + 4z) (3y – 4z) + (2y + 7z) (y + z)
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11C 31

Question 4.
The adjacent sides of a rectangle are x2 – 4xy + 7y2 and x3 – 5xy2. Find its area.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11C 32

Question 5.
The base and the altitude of a triangle are (3x – 4y) and (6x + 5y) respectively. Find its area.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11C 33

Question 6.
Multiply -4xy3 and 6x2y and verify your result for x = 2 and y= 1.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11C 34

Question 7.
Find the value of (3x3) x (-5xy2) x (2x2yz3) for x = 1, y = 2 and z = 3.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11C 35

Question 8.
Evaluate (3x4y2) (2x2y3) for x = 1 and y = 2.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11C 36

Question 9.
Evaluate (x5) × (3x2) × (-2x) for x = 1.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11C 37

Question 10.
If x = 2 and y = 1; find the value of (-4x2y3) × (-5x2y5).
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11C 38

Question 11.
Evaluate:
(i) (3x – 2)(x + 5) for x = 2.
(ii) (2x – 5y)(2x + 3y) for x = 2 and y = 3.
(iii) xz (x2 + y2) for x = 2, y = 1 and z= 1.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11C 39

Question 12.
Evaluate:
(i) x(x – 5) + 2 for x = 1.
(ii) xy2(x – 5y) + 1 for x = 2 and y = 1.
(iii) 2x(3x – 5) – 5(x – 2) – 18 for x = 2.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11C 40

Question 13.
Multiply and then verify :
-3x2y2 and (x – 2y) for x = 1 and y = 2.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11C 41

Question 14.
Multiply:
(i) 2x2 – 4x + 5 by x2 + 3x – 7
(ii) (ab – 1)(3 – 2ab)
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11C 42

Question 15.
Simplify : (5 – x)(6 – 5x)(2 -x).
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11C 43

Algebraic Expressions Exercise 11D – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Divide :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11D Q1
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11D 44
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11D 45
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11D 46
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11D 47
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11D 48
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11D 49
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11D 50
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11D 51
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11D 52

Question 2.
Find the quotient and the remainder (if any) when :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11D Q2
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11D 53
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11D 54
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11D 55

Question 3.
The area of a rectangle is x3 – 8x2 + 7 and one of its sides is x – 1. Find the length of the adjacent side.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11D 56

Question 4.
The product of two numbers is 16x4 – 1. If one number is 2x – 1, find the other.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11D 57

Question 5.
Divide x6 – y6 by the product of x2 + xy + y2 and x – y.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11D 58

Algebraic Expressions Exercise 11E – Selina Concise Mathematics Class 8 ICSE Solutions

Simplify :
Question 1.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E Q1
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E 59

Question 2.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E Q2
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E 60

Question 3.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E Q3
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E 61

Question 4.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E Q4
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E 62

Question 5.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E Q5
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E 63

Question 6.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E Q6
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E 64

Question 7.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E Q7
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E 65

Question 8.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E Q8
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E 66

Question 9.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E Q9
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E 67

Question 10.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E Q10
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E 68

Question 11.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E Q11
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E 69

Question 12.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E Q12
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E 70

Question 13.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E Q13
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E 71

Question 14.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E Q14
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E 72

Question 15.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E Q15
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions) Ex 11E 73

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations

Direct and Inverse Variations Exercise 10A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
In which of the following tables, x and y vary directly:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10A Q1
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10A 1
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10A 2

Question 2.
If x and y vary directly, find the values of x, y and z:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10A Q2
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10A 3

Question 3.
A truck consumes 28 litres of diesel for moving through a distance of 448 km. How much distance will it cover in 64 litres of diesel?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10A 4

Question 4.
For 100 km, a taxi charges ₹ 1,800. How much will it charge for a journey of 120 km?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10A 5

Question 5.
If 27 identical articles cost ₹ 1,890, how many articles can be bought for ₹ 1,750?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10A 6

Question 6.
7 kg of rice costs ₹ 1,120. How much rice can be bought for ₹ 3,680?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10A 7

Question 7.
6 note-books cost ₹ 156, find the cost of 54 such note-books.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10A 8

Question 8.
22 men can dig a 27 m long trench in one day. How many men should be employed for digging 135 m long trench of the same type in one day?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10A 9

Question 9.
If the total weight of 11 identical articles is 77 kg, how many articles of the same type would weigh 224 kg?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10A 10

Question 10.
A train is moving with uniform speed of 120 km per hour.
(i) How far will it travel in 36 minutes?
(ii) In how much time will it cover 210 km?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10A 11

Direct and Inverse Variations Exercise 10B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Check whether x and y vary inversely or not.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10B Q1
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10B 12

Question 2.
If x and y vary inversely, find the values of l, m and n :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10B Q2
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10B 13

Question 3.
36 men can do a piece of work in 7 days. How many men will do the same work in 42 days?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10B 14

Question 4.
12 pipes, all of the same size, fill a tank in 42 minutes. How long will it take to fill the same tank, if 21 pipes of the same size are used?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10B 15

Question 5.
In a fort 150 men had provisions for 45 days. After 10 days, 25 men left the fort. How long would the food last at the same rate?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10B 16

Question 6.
72 men do a piece of work in 25 days. In how many days will 30 men do the same work?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10B 17

Question 7.
If 56 workers can build a wall in 180 hours, how many workers will be required to do the same work in 70 hours?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10B 18

Question 8.
A car takes 6 hours to reach a destination by travelling at the speed of 50 km per hour. How long will it take when the car travels at the speed of 75 km per hour?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10B 19

Direct and Inverse Variations Exercise 10C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Cost of 24 identical articles is Rs. 108, Find the cost of 40 similar articles.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10C 20

Question 2.
If 15 men can complete a piece of work in 30 days, in how many days will 18 men complete it?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10C 21

Question 3.
In order to complete a work in 28 days, 60 men are required. How many men will be required if the same work is to be completed in 40 days?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10C 22

Question 4.
A fort had provisions for 450 soldiers for 40 days. After 10 days, 90 more soldiers come to the fort. Find in how many days will the remaining provisions last at the same rate?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10C 23

Question 5.
A garrison has sufficient provisions for 480 men for 12 days. If the number of men is reduced by 160; find how long will the provisions last.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10C 24

Question 6.
\(\frac { 3 }{ 5 }\) quintal of wheat costs Rs.210. Find the cost of :
(i) 1 quintal of wheat
(ii) 0.4 quintal of wheat
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10C 25

Question 7.
If \(\frac { 2 }{ 9 }\) of a property costs Rs.2,52,000; find the cost of \(\frac { 4 }{ 7 }\) of it.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10C 26

Question 8.
4 men or 6 women earn Rs. 360 in one day. Find, how much will:
(i) a man earn in one day?
(ii) a woman earn in one day?
(iii) 6 men and 4 women earn in one day?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10C 27

Question 9.
16 boys went to the canteen to have tea and snacks together. The bill amounted to Rs. 114.40. What will be the contribution of a boy who pays for himself and 5 others?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10C 28

Question 10.
50 labourers can dig a pond in 16 days. How many labourers will be required to dig another pond, double in size in 20 days?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10C 29

Question 11.
If 12 men or 18 women can complete a piece of work in 7 days, in how many days can 4 men and 8 women complete the same work?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10C 30

Question 12.
If 3 men or 6 boys can finish a work in 20 days, how long will 4 men and 12 boys take to finish the same work ?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10C 31

Question 13.
A particular work can be completed by 6 men and 6 women in 24 days; whereas the same work can be completed by 8 men and 12 women in 15 days. Find :
(i) according to the amount of work done, one man is equivalent to how many women.
(ii) the time taken by 4 men and 6 women to complete the same work.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10C 32
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10C 33

Question 14.
If 12 men and 16 boys can do a piece of work in 5 days and, 13 men and 24 boys can do it in 4 days, how long will 7 men and 10 boys take to do it?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10C 34

Direct and Inverse Variations Exercise 10D – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Eight oranges can be bought for Rs. 10.40. How many more can be bought for Rs. 16.90?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10D 35

Question 2.
Fifteen men can build a wall in 60 days. How many more men are required to build another wall of same size in 45 days?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10D 36

Question 3.
Six taps can fill an empty cistern in 8 hours. How much more time will be taken, if two taps go out of order? Assume, all the taps supply water at the same rate.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10D 37

Question 4.
A contractor undertakes to dig a canal, 6 kilometres long, in 35 days and employed 90 men. He finds that after 20 days only 2 km of canal have been completed. How many more men must be employed to finish the work in time?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10D 38

Question 5.
If 10 horses consume 18 bushels in 36 days. How long will 24 bushels last for 30 horses?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10D 39

Question 6.
A family of 5 persons can be main¬tained for 20 days with Rs.2,480. Find, how long Rs.6944 maintain a family of 8 persons
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10D 40

Question 7.
90 men can complete a work in 24 days working 8 hours a day. How many men are required to complete the same work in 18 days working 7\(\frac { 1 }{ 2 }\) hours a day?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10D 41

Question 8.
Twelve typists, all working with same speed, type a certain number of pages in 18 days working 8 hours a day. Find, how many hours per day must sixteen typists work in order to type the same number of pages in 9 days?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10D 42

Question 9.
If 25 horses consume 18 quintal in 36 days, how long will 28 quintal last for 30 horses?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10D 43

Question 10.
If 70 men dig 15,000 sq. m of a field in 5 days, how many men will dig 22,500 sq. m field in 25 days?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10D 44

Question 11.
A contractor undertakes to build a wall 1000 m long in 50 days. He employs 56 men, but at the end of 27 days, he finds that only 448 m of wall is built. How many extra men must the contractor employ so that the wall is completed in time ?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10D 45

Question 12.
A group of labourers promises to do a piece of work in 10 days, but five of them become absent. If the remaining labourers complete the work in 12 days, find their original number in the group.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10D 46

Question 13.
Ten men, working for 6 days of 10 hours each, finish \(\frac { 5 }{ 21 }\) of a piece of work. How many men working at the same rate and for the same number of hours each day, will be required to complete the remaining work in 8 days?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10D 47

Direct and Inverse Variations Exercise 10E – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
A can do a piece of work in 10 days and B in 15 days. How long will they take together to finish it ?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10E 48

Question 2.
A and B together can do a piece of work in 6\(\frac { 2 }{ 3 }\) days ; but B alone can do it in 10 days. How long will A take to do it alone?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10E 49

Question 3.
A can do a work in 15 days and B in 20 days. If they together work on it for 4 days ; what fraction of the work will be left ?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10E 50

Question 4.
A, B and C can do a piece of work in 6 days, 12 days and 24 days respectively. In what time will they all together do it?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10E 51

Question 5.
A and B working together can mow a field in 56 days and with the help of C, they could have mowed it in 42 days. How long would C take by himself?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10E 52

Question 6.
A can do a piece of work in 24 days, A and B can do it in 16 days and A, B and C in 10\(\frac { 2 }{ 3 }\) days. In how many days can A and C do it?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10E 53

Question 7.
A can do a piece of work in 20 days and B in 15 days. They worked together on it for 6 days and then A left. How long will B take to finish the remaining work?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10E 54

Question 8.
A can finish a piece of work in 15 days and B can do it in 10 days. They worked together for 2 days and then B goes away. In how many days will A finish the remaining work?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10E 55

Question 9.
A can do a piece of work in 10 days ; B in 18 days; and A, B and C together in 4 days. In what time would C alone do it ?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10E 56

Question 10.
A can do \(\frac { 1 }{ 4 }\) of a work in 5 days and B can do \(\frac { 1 }{ 3 }\) of the same work in 10 days. Find the number of days in which both working together will complete the work.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10E 57

Question 11.
One tap can fill a cistern in 3 hours and the waste pipe can empty the full cistern in 5 hours. In what time will the empty cistern be full, if the tap and the waste pipe are kept open together?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10E 58

Question 12.
A and B can do a work in 8 days; B and C in 12 days, and A and C in 16 days. In what time could they do it, all working together?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10E 59

Question 13.
A and B complete a piece of work in 24 days. B and C do the same work in 36 days ; and A, B and C together finish it in 18 days. In how many days will (i) A alone,
(ii) C alone,
(iii) A and C together, complete the work?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10E 60

Question 14.
A and B can do a piece of work in 40 days; B and C in 30 days; and C and A in 24 days.
(i) How long will it take them to do the work together?
(ii) In what time can each finish it working alone?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10E 61
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10E 62

Question 15.
A can do a piece of work in 10 days, B in 12 days and C in 15 days. All begin together but A leaves the work after 2 days and B leaves 3 days before the work is finished. How long did the work last?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10E 63
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10E 64

Question 16.
Two pipes P and Q would fill an empty cistern in 24 minutes and 32 minutes respectively. Both the pipes being opened together, find when the first pipe must be turned off so that the empty cistern may be just filled in 16 minutes.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations Ex 10E 65

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest

Simple and Compound Interest Exercise 9A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Find the interest and the amount on:
(i) ₹ 750 in 3 years 4 months at 10% per annum.
(ii) ₹ 5,000 at 8% per year from 23rd December 2011 to 29th July 2012.
(iii) ₹ 2,600 in 2 years 3 months at 1% per month.
(iv) ₹ 4,000 in 1\(\frac { 1 }{ 3 }\) years at 2 paise per rupee per month.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9A 1
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9A 2

Question 2.
Rohit borrowed Rs. 24,000 at 7.5 percent per year. How much money will he pay at the end of 4th years to clear his debt?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9A 3

Question 3.
The interest on a certain sum of money is Rs. 1,480 in 2 years and at 10 percent per year. Find the sum of money.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9A 4

Question 4.
On what principal will the simple interest be Rs. 7,008 in 6 years 3 months at 5% per year?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9A 5

Question 5.
Find the principal which will amount to Rs. 4,000 in 4 years at 6.25% Per annum.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9A 6

Question 6.
(i) At what rate per cent per annum will Rs. 630 produce an interest of Rs. 126 in 4 years ?
(ii) At what rate per cent per year will a sum double itself in 6\(\frac { 1 }{ 4 }\) years ?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9A 7

Question 7.
(i) In how many years will Rs.950 produce Rs.399 as simple interest at 7%?
(ii) Find the time in which Rs.1200 will amount to Rs.1536 at 3.5% per year.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9A 8

Question 8.
The simple interest on a certain sum of money is \(\frac { 3 }{ 8 }\) of the sum in 6\(\frac { 1 }{ 4 }\) years. Find the rate percent charged.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9A 9

Question 9.
What sum of money borrowed on 24th May will amount to Rs. 10210.20 on 17th October of the same year at 5 percent per annum simple interest.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9A 10
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9A 11

Question 10.
In what time will the interest on a certain sum of money at 6% be \(\frac { 5 }{ 8 }\) of itself?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9A 12

Question 11.
Ashok lent out Rs.7000 at 6% and Rs.9500 at 5%. Find his total income from the interest in 3 years.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9A 13

Question 12.
Raj borrows Rs.8,000; out of which Rs. 4500 at 5% and the remainder at 6%. Find the total interest paid by him in 4 years.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9A 14

Question 13.
Mohan lends Rs.4800 to John for 4\(\frac { 1 }{ 2 }\) years and Rs.2500 to Shy am for 6 years and receives a total sum of Rs.2196 as interest. Find the rate percent per annum, it being the same in both the cases.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9A 15
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9A 16

Question 14.
John lent Rs. 2550 to Mohan at 7.5 percent per annum. If Mohan discharges the debt after 8 months by giving an old black and white television and Rs. 1422.50; find the price of the television.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9A 17

Simple and Compound Interest Exercise 9B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
The interest on a certain sum of money is 0.24 times of itself in 3 years. Find the rate of interest.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9B 18

Question 2.
If ₹ 3,750 amount to ₹ 4,620 in 3 years at simple interest. Find:
(i) the rate of interest
(ii) the amount of Rs. 7,500 in 5\(\frac { 1 }{ 2 }\) years at the same rate of interest
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9B 19

Question 3.
A sum of money, lent out at simple interest, doubles itself in 8 years. Find :
(i) the rate of interest
(ii) in how many years will the sum become triple (three times) of itself at the same rate percent?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9B 20

Question 4.
Rupees 4000 amount to Rs.5000 in 8 years ; in what time will Rs.2100 amount to Rs.2800 at the same rate ?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9B 21

Question 5.
What sum of money lent at 6.5% per annum will produce the same interest in 4 years as Rs.7500 produce in 6 years at 5% per annum?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9B 22

Question 6.
A certain sum amounts to Rs.3825 in 4 years and to Rs.4050 in 6 years. Find the rate percent and the sum.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9B 23

Question 7.
At what rate percent of simple interest will the interest on Rs.3750 be one-fifth of itself in 4 years? To what will it amount in 15 years?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9B 24
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9B 25

Question 8.
On what date will ₹ 1950 lent on 5th January 2011 amount to ₹ 2125.50 at 5 percent per annum simple interest?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9B 26

Question 9.
If the interest on Rs.2400 is more than the interest on Rs.2000 by Rs.60 in 3 years at the same rate percent; find the rate.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9B 27
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9B 28

Question 10.
Divide Rs. 15,600 into two parts such that the interest on one at 5 percent for 5 years may be equal to that on the other at 4\(\frac { 1 }{ 2 }\) per cent for 6 years.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9B 29

Simple and Compound Interest Exercise 9C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
A sum of Rs. 8,000 is invested for 2 years at 10% per annum compound interest. Calculate:
(i) interest for the first year.
(ii) principal for the second year.
(iii) interest for the second year.
(iv) final amount at the end of second year
(v) compound interest earned in 2 years.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 30

Question 2.
A man borrowed Rs. 20,000 for 2 years at 8% per year compound interest. Calculate :
(i) the interest of the first year.
(ii) the interest of the second year.
(iii) the final amount at the end of second year.
(iv) the compound interest of two years.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 31

Question 3.
Calculate the amount and the compound interest on Rs. 12,000 in 2 years and at 10% per year.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 32

Question 4.
Calculate the amount and the compound interest on Rs. 10,000 in 3 years at 8% per annum.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 33

Question 5.
Calculate the compound interest on Rs. 5,000 in 2 years; if the rates of interest for successive years be 10% and 12% respectively.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 34

Question 6.
Calculate the compound interest on Rs. 15,000 in 3 years; if the rates of interest for successive years be 6%, 8% and 10% respectively.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 35

Question 7.
Mohan borrowed Rs. 16,000 for 3 years at 5% per annum compound interest. Calculate the amount that Mohan will pay at the end of 3 years.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 36

Question 8.
Rekha borrowed Rs. 40,000 for 3 years at 10% per annum compound interest. Calculate the interest paid by her for the second year.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 37

Question 9.
Calculate the compound interest for the second year on Rs. 15000 invested for 5 years at 6% per annum.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 38

Question 10.
A man invests Rs. 9600 at 10% per annum compound interest for 3 years. Calculate :
(i) the interest for the first year.
(ii) the amount at the end of the first year.
(iii) the interest for the second year.
(iv) the interest for the third year.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 39

Question 11.
A person invests Rs. 5,000 for two years at a certain rate of interest compounded annually. At the end of one year, this sum amounts to Rs. 5,600. Calculate :
(i) the rate of interest per year.
(ii) the amount at the end of the second year.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 40

Question 12.
Calculate the difference between the compound interest and the simple interest on ₹ 7,500 in two years and at 8% per annum.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 41

Question 13.
Calculate the difference between the compound interest and the simple interest on ₹ 8,000 in three years and at 10% per annum.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 42

Question 14.
Rohit borrowed ₹ 40,000 for 2 years at 10% per annum C.I. and Manish borrowed the same sum for the same time at 10.5% per annum simple interest. Which of these two gets less interest and by how much?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 43

Question 15.
Mr. Sharma borrowed ₹ 24,000 at 13% p.a. simple interest and an equal sum at 12% p.a. compound interest. Find the total interest earned by Mr. Sharma in 2 years.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 44

Question 16.
Peter borrows ₹ 12,000 for 2 years at 10% p.a. compound interest. He repays ₹ 8,000 at the end of first year. Find:
(i) the amount at the end of first year, before making the repayment.
(ii) the amount at the end of first year, after making the repayment.
(iii) the principal for the second year.
(iv) the amount to be paid at the end of second year, to clear the account.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 45

Question 17.
Gautam takes a loan of ₹ 16,000 for 2 years at 15% p.a. compound interest. He repays ₹ 9,000 at the end of first year. How mucH must he pay at the end of second year to clear the debt?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 46

Question 18.
A certain sum of money, invested for 5 years at 8% p.a. simple interest earns an interest of ₹ 12,000. Find:
(i) the sum of money.
(ii) the compound interest earned by this money in two years and at 10% p.a. compound interest.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 47

Question 19.
Find the amount and the C.I. on ₹ 12,000 at 10% per annum compounded half-yearly.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 48

Question 20.
Find the amount and the C.I. on ₹ 8,000 in 1\(\frac { 1 }{ 2 }\) years at 20% per year compounded half- yearly.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 49

Question 21.
Find the amount and the compound interest on ₹ 24,000 for 2 years at 10% per annum compounded yearly.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 50

Question 22.
Find the amount and the compound interest on ₹ 16,000 for 3 years at 5% per annum compounded annually.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 51

Question 23.
Find the amount and the compound interest on ₹ 20,000 for 1\(\frac { 1 }{ 2 }\) years at 10% per annum compounded half-yearly.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 52

Question 24.
Find the amount and the compound interest on ₹ 32,000 for 1 year at 20% per annum compounded half-yearly.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 53

Question 25.
Find the amount and the compound interest on ₹ 4,000 in 2 years, if the rate of interest for first year is 10% and for the second year is 15%.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 54

Question 26.
Find the amount and the compound interest on ₹ 10,000 in 3 years, if the rates of interest for the successive years are 10%, 15% and 20% respectively.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest Ex 9C 55

Selina Concise Mathematics Class 8 ICSE Solutions