## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Check Your Progress

Question 1.
Each student from the group of 40 students was asked to roll a dice independently. The results are given below:
2, 3, 3, 4, 1, 5, 2, 6, 1, 4, 2, 3, 4, 4, 6, 1, 5, 5, 2, 4, 5, 5, 3, 1, 6, 5, 4, 2, 3, 6, 1, 1, 4, 4, 5, 3, 2, 2, 6,6
Make a frequency distribution table for the same.
Solution:

Question 2.
The marks obtained by 30 students of a class in a test of maximum marks 20 are as follows:
15, 11, 12, 10, 9, 8, 19, 13, 16, 3, 2, 17, 18, 19, 14, 6, 20, 15, 16, 12, 10, 4, 9, 8, 12, 17, 18, 20, 19, 12.
Prepare a frequency distribution table for the above data using class intervals 0-4, 4-8 and so on.
Solution:

Question 3.
Construct a frequency distribution table for the following weights (in grams) of 35 oranges, using class intervals 40—45, 45-50 and so on.
30, 40, 45, 32, 43, 50, 55, 63, 72, 73, 62, 61, 54, 53, 50, 43, 76, 38, 54, 55, 66, 70, 74, 75, 45, 47, 59, 58, 60, 63, 74, 33, 35, 70, 68.
(i) How many classes are there in the frequency distribution table?
(ii) Which weight group has the lowest frequency?
(iii) Which weight group has the highest frequency?
Solution:

Question 4.
Draw a histogram of the following data:
Marks obtained by students in a Mathematics Paper of maximum marks 100.

Solution:

Question 5.
The following data represents the number of students using a different mode of transportation to come to school.

Draw a pie chart to represent this data Pie chart is given below:
Solution:

Question 6.
Answer the following questions based on the pie chart given below:
(i) Which type of programmes are viewed the most?
(ii) Which type of programmes are viewed the least?
(iii) Which two types of programmes have number of viewers equal to those watching sports channels?

Solution:

Question 7.
Suppose you spin the wheel shown in adjoining figure.
(i) List the outcomes of getting a green sector and not getting a green sector on this wheel.
(ii) Find the probability of getting a green sector.
(iii) Find the probability of not getting a green sector.

Solution:

Question 8.
A bag has 4 red and 2 yellow balls. A ball is drawn from the bag without looking into the bag. What is the probability of getting
(i) a red ball?
(ii) not a red ball?
Solution:

Question 9.
Three coins are tossed together, find the probability of getting
Solution:

Question 10.
A letter is chosen from the word ‘RECTANGLE’. What is the probability that it is
(i) a consonant
(ii) not a consonant.
Solution:

## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) Bar graphs are ……….. representation of ungrouped data.
(ii) In a grouped frequency distribution, the difference between lower limit and upper limit of a class is called ………..
(iii) The mid point of the class interval is called ………..
(iv) Bar graphs of grouped data are called ………..
(v) The circle graphs are commonly called ………..
(vi) An experiment which has more than one possible outcomes and it is not possible to predict the outcome in advance is called ………..
(vii) The outcomes which ensures the occurrence of an event are called ………..
(viii) An event which never happens is called ………..
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) The data arranged in ascending or descending order of size is called data array.
(ii) The lower limit of class 10-20 is 20.
(iii) The class size of class 20-30 is 10.
(iv) The class mark of 25-35 is 30.
(v) There is no difference between bar graphs and histograms.
(vi) In histograms the breadth of a rectangle is meaningless.
(vii) In histograms, there is no gap between two adjacent rectangle.
(viii) In a pie chart, size of each sector is proportional to the value of item represented by it.
(ix) In a pie chaiangle of sector
= $$\frac{\text { value of item }}{\text { sum of values of all items }} \times 180^{\circ}$$
(x) In tossing a coin getting head or tail are equally likely events.
(xi) Probability of an event E satisfies 0 ≤ P(E) ≤ 1.
(xii) P(occurrence of an event) = P(non occurence of an event).
(xiii) Total number of outcomes when two dice are rolled togehter = 6 + 6.
Solution:

Multiple Choice Questions
Study the following frequency distribution table:
The table shows the pocket money (in ?) per month of 50 students. Choose the correct answer from the given four options for questions 3 to 7;

Question 3.
Size of the class-intervals is
(a) 50
(b) 20
(c) 10
(d) 30
Solution:

Question 4.
The class having the maximum frequency is
(a) 10-20
(b) 20-30
(c) 30-40
(d) 40-50
Solution:

Question 5.
The upper limit of the class having minimum frequency is
(a) 30
(b) 40
(c) 50
(d) 60
Solution:

Question 6.
Which two are classes having the same frequency?
(a) 10-20 and 20-30
(b) 20-30 and 30-40
(c) 30-40 and 50-60
(d) 40-50 and 50-60
Solution:

Question 7.
The frequency of class whose class mark is 25 is
(a) 14
(b) 11
(c) 10
(d) 4
Solution:

The pie graph shown in the adjoining figure representing the different subjects liked by the students of class VIII. Study the pie graph carefully and choose the correct answer from the given four options for questions 8 to 11.

Question 8.
Which subject is liked by the maximum number of students
(a) Maths
(b) Science
(c) S. Science
(d) English
Solution:

Question 9.
Which subject is liked by the minimum number of students
(a) Maths
(b) Science
(c) S. Science
(d) English
Solution:

Question 10.
If there are 200 students in class VIII then the number of students who like S. Science
(a) 10
(b) 20
(c) 40
(d) 80
Solution:

Question 11.
Number of students who like Science
(a) 20
(b) 40
(c) 60
(d) 80
Solution:

Choose the correct answer from the given four options (12 to 17):
Question 12.
Probability of getting the sum as 4 when a pair of dice is rolled

Solution:

Question 13.
Probability of getting exactly 2 heads when three coins are tossed together

Solution:

Question 14.
Probability of selecting a consonant from the letters of the word ‘FATHER’

Solution:

Question 15.
Probability of getting more than 2 heads when a pair of coins is tossed.
(a) 1
(b) $$\frac{1}{2}$$
(c) $$\frac{1}{3}$$
(d) 0
Solution:

Question 16.
Probability of getting a red ball from a bag containing 20 red balls
(a) 0
(b) 1
(c) $$\frac{1}{20}$$
(d) $$\frac{1}{2}$$
Solution:

Question 17.
Probability of getting a non-red ball from a bag containing 4 red, 5 blue and 3 black balls is

Solution:

Value Based Questions
Question 1.
Draw a pie chart of the data given below:
The time spent by a Class VIII student during a day.

Should a student of class VIII study for just 2 hours daily? Which time is considered the best time for self-study?
Solution:

Question 2.
From a bag containing 2 saffron, 3 white and 4 green balls a ball is drawn at random. Find the probability that ball drawn is
(i) Saffron
(ii) White
(iii) Green
Which are three colours in our National Flag? What values did they indicate? What values are being promoted?
Solution:

Question 3.
Four defective oranges are accidentally mixed with 16 good ones. One orange is drawn at random. Find the probability that the orange drawn is good one.
What will happen if 4 bad persons are mixed with 16 good ones?
Solution:

Higher Order Thinking Skills (Hots)
Question 1.
A bag contains 12 balls out of which x are black.
(i) If a ball drawn at random, what is the probability that it will be a black ball?
(ii) If 6 more black balls are put in the bag, the probability of drawing a black ball will be double than that of (i). Find the value of x.
Solution:

Question 2.
Ankita and Nagma are friends. They were both born in 1998. What is the probability that they have
(i) same birthday?
(ii) different birthday?
Solution:

## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.3

Question 1.
List the outcomes you can see in these experiments.

Solution:

Question 2.
A die is rolled once. Find the probability of getting
(i) an even number
(ii) a multiple of 3
(iii) not a multiple of 3
Solution:

Question 3.
Two coins are tossed together. Find the probability of getting
(i) two tails
(ii) atleast one tail
(iii) no tail
Solution:

Question 4.
Three coins are tossed together. Find the probability of getting
(ii) atleast one tail
(iii) atmost one tail.
Solution:

Question 5.
Two dice are rolled simultaneously. Find the probability of getting
(i) the sum as 7
(ii) the sum as 3 or 4
(iii) prime numbers on both the dice.
Solution:

Question 6.
A fcox contains 600 screws, one tenth are rusted. One screw is taken out at random from the box. Find the probability that it is
(i) a rusted screw
(ii) not a rusted screw
Solution:

Question 7.
A letter is chosen from the word ‘TRIANGLE’. What is the probability that it is a vowel?
Solution:

Question 8.
A bag contains 5 red, 6 black and 4 white balls. A ball is drawn at random from the bag, find the probability the ball is drawn is
(i) white
(ii) not black
(iii) red or black
(iv) neither red nor black
Solution:

Question 9.
A box contains 17 cards numbered 1, 2, 3, ……….,17 and are mixed thoroughly. A card is drawn at random from the box. Find the probability that the number on the card is
(i) odd
(ii) even
(iii) prime
(iv) divisible by 3
(v) divisible by 2 and 3 both
Solution:

Question 10.
A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is:
(i) an ace
(ii) a red card
(iii) neither a king nor a queen
(iv) a red face card or an ace
(vi) non-face card of red colour.
Solution:

Question 11.
In a lottery, there are 5 prized tickets and 995 blank tickets. A person buys a lottery ticket. Find the probability of his winning a prize.
Solution:

## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.2

Question 1.
The following data represents the different number of animals in a zoo. Prepare a pie chart for the given data.

Solution:

Question 2.
The following data represents the monthly expenditure of a family (in T) on various items. Draw a pie chart to represent this data.

Solution:

Question 3.
The following data represents the percentage distribution of the expenditure incurred in publishing a book.

Draw a pie chart to represent this data.
Solution:

Question 4.
The following data represents the number of students got admission in different streams of a college:

Draw a pie chart to represent this data.
Solution:

Question 5.
The adjoining pie chart shows the expenditure of a country on various sports during year 2012. Study the pie chart carefully and answer the following questions:

(i) What percent of total expenditure is spent on cricket?
(ii) How much percent more is spent on hockey than that on tennis?
(iii) If the total amount spent on sports in 2012 is ₹1,80,00,000, then find amount spent on Badminton,
(iv) If the total amount spent on sports in 2012 is ₹2,40,00,000 then find the amount spent on cricket and hockey together.
Solution:

Question 6.
The adjoining pie chart shows the number of students enrolled in class VI to class X of a school.

If 1440 students are enrolled from VI to X, then answer the following questions:
(i) How many students are enrolled in class VIII?
(ii) How many students are more in class IX than in class X?
(iii) What is the sum of students enrolled in VII and VIII?
(iv) Find the ratio of students enrolled in VI to students enrolled in X.
Solution:

## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1

Question 1.
The result of a survey of 200 people about their favourite fruit is given below:

Represent the above data by a bar graph.
Solution:

Question 2.
Mr Khurana has two kitchen appliance stores. He compares the sales of two stores during a month and recovered as given below:

Represent the above data by a double bar graph.
Solution:

Question 3.
The number of goals scored by a football team in different matches is given below:
3, 1, 0, 4, 6, 0, 0, 1, 1, 2, 2, 3, 5, 1, 2, 0, 1, 0, 2, 3, 9, 2, 0, 1, 0, 1, 4, 1, 0, 2, 5, 1, 2, 2, 3, 1, 0, 0, 0, 1, 1, 0, 2, 3, 0, 1, 5, 2, 0
Make a frequency distribution table using tally marks.
Solution:

Question 4.
Given below a bar graph:

(i) What is the information given by the bar graph?
(ii) On which item the expenditure is maximum?
(iii) On which item the expenditure is minimum?
(iv) State whether true or false:
Expenditure on education is twice the expenditure on clothing.
Solution:

Question 5.
Given below a double bar graph.

(i) What is the information given by the double graph?
(ii) Which mode of transport girls using more than the boys?
(iii) Which mode of transport boys using the most?
(iv) In which mode of transport number of girls is half the number of boys?
Solution:

Question 6.
Using class intervals 0-5, 5-10, construct the frequency distribution table for the following
data:
13, 6, 12, 9, 11, 14, 2, 8, 18, 16, 9, 13, 17, 11, 19, 6, 7, 12, 22, 21, 18, 1, 8, 12, 18.
Solution:

Question 7.
Given below are the marks secured by 35 students in a surprise test:
41, 32, 35, 21, 11, 47, 42, 00, 05, 18, 25, 24, 29, 38, 30, 04, 14, 24, 34, 44, 48, 33, 36, 38, 41, 48, 08, 34, 39, 11, 13, 27, 26, 43, 03.
Taking class intervals 0-10, 10-20, …….. construct frequency distribution table. Find the number
of students obtaining below 20 marks.
Solution:

Question 8.
The electricity bills (in ?) of 40 houses in a locality are given below:
78, 87,81,52, 59, 65, 101, 108, 115, 95, 98, 65,62, 121, 128, 63,76, 84, 89,91,65, 101,95,81, 87, 105, 129, 92, 75, 105, 78, 72, 107, 116, 127, 100, 80, 82, 61, 118 Construct a grouped frequency distribution table of class size 10.
Class intervals (Electricity bill in ?) Tally marks Frequency (Number of houses)
Solution:

Question 9.
Draw a histogram for the frequency table made for data in Question 8, and answer the following questions:
(i) Which group has the maximum number of houses?
(ii) How many houses pay less than ₹ 100?
(iii) How many houses pay ₹ 100 or more?
Solution:

Question 10.
The weights of 29 patients in a hospital were recorded as follows:

Draw a histogram to represent this data visually.
Solution:

Question 11.
In a study of diabetic patients, the following data was obtained:

Represent the above data by a histogram.
Solution:

Question 12.
The histogram showing the weekly wages (in ₹) of workers in a factory is given alongside:

(i) What is the frequency of class 400-425?
(ii) What is the class having a minimum frequency?
(iii) How many workers get more than ₹425?
(iv) How many workers get less than ₹475?
(v) Number of workers whose weekly wages are more than or equal to ₹400 but less than ₹450.
Solution:

Question 13.
The number of hours for which students of a particular class watched television during holidays is shown in the histogram below.

(i) For how many hours did the maximum number of students watch T.V.?
(ii) How many students watched T.V. for less than 4 hours?
(iii) How many students spent more than 5 hours in watching T.V.?
(iv) How many students spent more than 2 hours but less than 4 hours in watching T.V.?
Solution:

Question 14.
The number of literate females in the age group of 10 to 40 years in a town is shown in the histogram alongside.

(i) Write the classes assuming all the classes are of equal width.
(ii) What is the class size?
(iii) In which age group are the literate females the least?
(iv) In which age group is the number of literate females the highest?
Solution:

## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) Area of a parallelogram = base × …….
(ii) Area of a trapezium = $$\frac{1}{2}$$ × ……….. × distance between parallel sides.
(iii) Area of a rhombus = $$\frac{1}{2}$$ × product of ……..
(iv) Area is measured in ……….. units.
(v) Volume of a solid is the measurement of ………… occupied by it.
(vi) Volume is measured in ………… units.
(vii) The volume of a unit cube is ……….
(viii) 1 litre = …………… cm3
(ix) 1 m3 = ………… litres
(x) Volume of a cuboid = ……….. × height.
(xi) Cylinders in which line segment joining the centres of the circular faces is perpendicular to the base are called ……….
(xii) Volume of a cylinder = area of base × ………..
(xiii) Area of four walls = perimeter of floor × …….
(xiv) Lateral surface area of a cube = 4 × (…………)2
(xv) Total surface area of a cylinder of radius r and height h is ………..
Solution:

Question 2.
State which of the following statements are true (T) or false (F):
(i) Perimeter of a rectangle is the sum of lengths of its four sides.
(ii) Area of a quadrilateral can be found by splitting it into two triangles.
(iiii) Perimeter of a circle of radius r = πr2.
(iv) Volume of a cube = 6 × (side)2
(v) 1 m3 = 100000 cm3
(vi) Total surface area of a cuboid
= 2 (lb + bh + hl)
(vii) There is no difference between volume and capacity.
(viii)Total surface area of a cylinder = lateral surface area + area of two circular ends.
(ix) Surface area of a cube = 4 × (side)2
(x) Lateral surface area of a cuboid = perimeter of base × height.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 17):
Question 3.
Area of a triangle is 30 cm2. If its base is 10 cm, then its height is
(a) 5 cm
(b) 6 cm
(c) 7 cm
(d) 8 cm
Solution:

Question 4.
If the perimeter of a square is 80 cm, then its area is
(a) 800 cm2
(b) 600 cm2
(c) 400 cm2
(d) 200 cm2
Solution:

Question 5.
Area of a parallelogram is 48 cm2. If its height is 6 cm then its base is
(a) 8 cm
(b) 4 cm
(c) 16 cm
(d) none of these
Solution:

Question 6.
If d is the diameter of a circle, then its area is
(a) πd2
(b) $$\frac{\pi d^{2}}{2}$$
(c) $$\frac{\pi d^{2}}{4}$$
(d) 2πd2
Solution:

Question 7.
If the area of a trapezium is 64 cm2 and the distance between parallel sides is 8 cm, then sum of its parallel sides is
(a) 8 cm
(b) 4 cm
(c) 32 cm
(d) 16 cm
Solution:

Question 8.
Area of a rhombus whose diagonals are 8 cm and 6 cm is
(a) 48 cm2
(b) 24 cm2
(c) 12 cm2
(d) 96 cm2
Solution:

Question 9.
If the lengths of diagonals of a rhombus is doubled, then area of rhombus will be
(a) doubled
(b) tripled
(c) four times
(d) remains same
Solution:

Question 10.
If the length of a diagonal of a quadrilateral is 10 cm and lengths of the perpendiculars on it from opposite vertices are 4 cm and 6 cm, then area of quadrilateral is
(a) 100 cm2
(b) 200 cm2
(c) 50 cm2
(d) none of these
Solution:

Question 11.
Area of a rhombus is 90 cm2. If the length of one diagonal is 10 cm then the length of other diagonal is
(a) 18 cm
(b) 9 cm
(c) 36 cm
(d) 4.5 cm
Solution:

Question 12.
If the volume of a cube is 729 cm3, then its surface area is
(a) 486 cm2
(b) 324 cm2
(c) 162 cm2
(d) none of these
Solution:

Question 13.
If the lateral surface area of a cube is 100 cm2, then its volume is
(a) 25 cm3
(b) 125 cm3
(c) 625 cm3
(d) none of these
Solution:

Question 14.
If the length of side of a cube is doubled, then the ratio of volumes of new cube and original cube is
(a) 1 : 2
(b) 2 : 1
(c) 4 : 1
(d) 8 : 1
Solution:

Question 15.
If the dimensions of a rectangular room are 10m × 12m × 9m, then the cost of painting its four walls at the rate of ₹8 per m2 is
(a) ₹3186
(b) ₹3618
(c) ₹3168
(d) none of these
Solution:

Question 16.
Volume of a cylinder is 1848 cm2. If the diameter of its base is 14 cm, then the height of the cylinder is
(a) 12 cm
(b) 6 cm
(c) 3 cm
(d) none of these
Solution:

Question 17.
If the radius of a cylinder is doubled and height is halved, then new volume is
(a) same
(b) 2 times
(c) 4 times
(d) 8 times
Solution:

Value Based Questions
Question 1.
Pulkit painted four walls and roof of a rectangular room of size 10m × 12m × 12m. He got ₹10 per m2 for his work. How much money did he earn? He always gives one-fourth of his income to an orphanage. Find how much money he gave to the orphanage? What values are being promoted?
Solution:

Question 2.
In a slogan writing competition in a school, Rama wrote the slogan ‘Truth pays, never betrays’ on a trapezium shaped cardboard. If the lengths of parallel sides of trapezium are 60 cm and 80 cm and the distance between them is 50 cm, find the area of trapezium. What are the advantages of speaking truth?
Solution:

Higher Order Thinking Skills (Hots)
Question 1.
The length of a room is 50% more than its breadth. The cost of carpeting the room at the rate of ₹38.50 m2 is ₹924 and the cost of papering the walls at ₹3.30 m2 is ₹214.50. If the room has one door of dimensions 1 m × 2 m and two windows each of dimensions 1 m × 1.5 m, find the dimensions of the room.
Solution:

Question 2.
The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen will be used up when writing 310 words on an average. How many words would use up a bottle of ink containing one-fifth of a litre? Answer correct to the nearest 100 words.
Solution:

Question 3.
A cylindrical jar is 20 cm high with an internal diameter 7 cm. An iron cube of edge 5 cm is immersed in the jar completely in the water which was originally 12 cm high. Find the rise in the level of water.
Solution:

Question 4.
Squares each of side 6 cm are cut off from the four comers of a sheet of tin measuring 42 cm by 30 cm. The remaining portion of the tin sheet is made into an open box by folding up the flaps. Find the capacity of the box.
Solution:

## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4

Question 1.
The surface area of a cube is 384 cm2. Find
(i) the length of an edge
(ii) volume of the cube.
Solution:

Question 2.
Find the total surface area of a solid cylinder of radius 5 cm and height 10 cm. Leave your answer in terms of n.
Solution:

Question 3.
An aquarium is in the form of a cuboid whose external measures are 70 cm × 28 cm × 35 cm. The base, side faces and back face are to be covered with coloured paper. Find the area of the paper needed.
Solution:

Question 4.
The internal dimensions of the rectangular hall are 15 m × 12 m × 4 m. There are 4 windows each of dimension 2 m × 1.5 m and 2 doors each of dimension 1.5 m × 2.5 m. Find the cost of whitewashing all four walls of the hall, if the cost of whitewashing is ₹5 per m2. What will be the cost of whitewashing if the ceiling of the hall is also whitewashed?
Solution:

Question 5.
A swimming pool is 50 m in length, 30 m in breadth and 2·5 m in depth. Find the cost of cementing its floor and walls at the rate of ₹27 per square metre.
Solution:

Question 6.
The floor of a rectangular hall has a perimeter 236 m. Its height is 4·5 m. Find the cost of painting its four walls (doors and windows be ignored) at the rate of Rs. 8.40 per square metre.
Solution:

Question 7.
A cuboidal fish tank has a length of 30 cm, a breadth of 20 cm and a height of 20 cm. The tank is placed on a horizontal table and it is three-quarters full of water. Find the area of the tank which is in contact with water.
Solution:

Question 8.
The volume of a cuboid is 448 cm3. Its height is 7 cm and the base is a square. Find
(i) a side of the square base
(ii) surface area of the cuboid.
Solution:

Question 9.
The length, breadth and height of a rectangular solid are in the ratio 5 : 4 : 2. If its total surface area is 1216 cm2, find the volume of the solid.
Solution:

Question 10.
A rectangular room is 6 m long, 5 m wide and 3·5 m high. It has 2 doors of size 1·1 m by 2 m and 3 windows of size 1·5 m by 1·4 m. Find the cost of whitewashing the walls and the ceiling of the room at the rate of ₹5·30 per square metre.
Solution:

Question 11.
A cuboidal block of metal has dimensions 36 cm by 32 cm by 0·25 m. It is melted and recast into cubes with an edge of 4 cm.
(i) How many such cubes can be made?
(ii) What is the cost of silver coating the surfaces of the cubes at the rate of ₹0·75 per square centimetre?
Solution:

Question 12.
Three cubes of silver with edges 3 cm, 4 cm and 5 cm are melted and recast into a single cube, find the cost of coating the surface of the new cube with gold at the rate of ₹3·50 per square centimetre?
Solution:

Question 13.
The curved surface area of a hollow cylinder is 4375 cm2, it is cut along its height and formed a rectangular sheet of width 35 cm. Find the perimeter of the rectangular sheet.
Solution:

Question 14.
A road roller has a diameter of 0.7 m and its width is 1.2 m. Find the least number of revolutions that the roller must take in order to level a playground of size 120 m × 44 m.
Solution:

Question 15.
A company packages its milk powder in cylindrical container whose base has a diameter of 14 cm and height 20 cm. Company places a label around the surface of the container (as shown in the figure). If the label is placed 2 cm from top and bottom, what is the area of the label?

Solution:

Question 16.
The sum of the radius and 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:

Question 17.
The ratio between the curved surface and total surface of a cylinder is 1 : 2. Find the volume of the cylinder, given that its total surface area is 616 cm3.
Solution:

Question 18.
The given figure showed a metal pipe 77 cm long. The inner diameter of the cross-section is 4 cm and the outer one is 4.4 cm.
Find its
(i) inner curved surface area
(ii) outer curved surface area
(iii) total surface area.

Solution:

## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.3

Question 1.
The volume of a cube is 343 cm3, find the length of an edge of cube.
Solution:

Question 2.
Fill in the following blanks:

Solution:

Question 3.
Find the height of a cuboid whose volume is 312 cm3 and base area is 26 cm2.
Solution:

Question 4.
A godown is in the form of a cuboid of measures 55 m × 45 m × 30 m. How many cuboidal boxes can be stored in it if the volume of one box is 1.25 m3?
Solution:

Question 5.
A rectangular pit 1.4 m long, 90 cm broad and 70 cm deep was dug and 1000 bricks of base 21 cm by 10.5 cm were made from the earth dugout. Find the height of each brick.
Solution:

Question 6.
If each edge of a cube is tripled, then find how many times will its volume become?
Solution:

Question 7.
A milk tank is in the form of cylinder whose radius is 1.4 m and height is 8 m. Find the quantity of milk in litres that can be stored in the tank.
Solution:

Question 8.
A closed box is made of 2 cm thick wood with external dimension 84 cm × 75 cm × 64 cm. Find the volume of the wood required to make the box.
Solution:

Question 9.
Two cylindrical jars contain the same amount of milk. If their diameters are in the ratio 3 : 4, find the ratio of their heights.
Solution:

Question 10.
The radius of the base of a right circular cylinder is halved and the height is doubled. What is the ratio of the volume of the new cylinder to that of the original cylinder?
Solution:

Question 11.
A rectangular piece of a tin of size 30 cm × 18 cm is rolled in two ways, once along its length (30 cm) and once along its breadth. Find the ratio of volumes of two cylinders so formed.
Solution:

Question 12.
Water flows through a cylindrical pipe of internal diameter 7 cm at 5 m per sec. Calculate
(i) the volume in litres of water discharged by the pipe in one minute.
(ii) the time in minutes, the pipe would take to fill an empty rectangular tank of size 4 m × 3 m × 2.31 m.
Solution:

Question 13.
Two cylindrical vessels are filled with milk. The radius of one vessel is 15 cm and the height is 40 cm, and the radius of other vessel is 20 cm and the height is 45 cm. Find the radius of another cylindrical vessel of height 30 cm which may just contain the milk which is in the two given vessels.
Solution:

Question 14.
A wooden pole is 7 m high and 20 cm in diameter. Find its weight if the wood weighs 225 kg per m3 .
Solution:

Question 15.
A cylinder of the maximum volume is cut from a wooden cuboid of length 30 cm and cross-section a square of side 14 cm. Find the volume of the cylinder and the volume of the wood wasted.
Solution:

## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.2

Question 1.
Each side of a rhombus is 13 cm and one diagonal is 10 cm. Find
(i) the length of its other diagonal
(ii) the area of the rhombus
Solution:

Question 2.
The cross-section ABCD of a swimming pool is a trapezium. Its width AB = 14 m, depth at the shallow end is 1-5 m and at the deep end is 8 m. Find the area of the cross-section.

Solution:

Question 3.
The area of a trapezium is 360 m2, the distance between two parallel sides is 20 m and one of the parallel side is 25 m. Find the other parallel side.
Solution:

Question 4.
Find the area of a rhombus whose side is 6.5 cm and altitude is 5 cm. If one of its diagonal is 13 cm long, find the length of other diagonal.
Solution:

Question 5.
From the given diagram, calculate
(i) the area of trapezium ACDE
(ii) the area of parallelogram ABDE
(iii) the area of triangle BCD.

Solution:

Question 6.
The area of a rhombus is equal to the area of a triangle whose base and the corresponding altitude are 24.8 cm and 16.5 cm respectively. If one of the diagonals of the rhombus is 22 cm, find the length of the other diagonal.
Solution:

Question 7.
The perimeter of a trapezium is 52 cm. If its non-parallel sides are 10 cm each and its altitude is 8 cm, find the area of the trapezium.
Solution:

Question 8.
The area of a trapezium is 540 cm2. If the ratio of parallel sides is 7 : 5 and the distance between them is 18 cm, find the lengths of parallel sides.
Solution:

Question 9.
Calculate the area enclosed by the given shapes. All measurements are in cm.

Solution:

Question 10.
(ii) the area of trapezium ABCD
(iii) the area of triangle BCD

Solution:

Question 11.
Diagram of the adjacent picture frame has outer dimensions = 28 cm × 32 cm and inner dimensions 20 cm × 24 cm. Find the area of each section of the frame, if the width of each section is same.

Solution:

Question 12.
In the given quadrilateral ABCD, ∠BAD = 90° and ∠BDC = 90°. All measurements are in centimetres. Find the area of the quadrilateral ABCD.

Solution:

Question 13.
Top surface of a raised platform is in the shape of a regular octagon as shown in the given figure. Find the area of the octagonal surface.

Solution:

Question 14.
There is a pentagonal shaped park as shown in the following figure:
For finding its area Jaspreet and Rahul divided it in two different ways.

Find the area of this park using both ways. Can you suggest some other way of finding its area?
Solution:

Question 15.
In the diagram, ABCD is a rectangle of size 18 cm by 10 cm. In ∆ BEC, ∠E = 90° and EC = 8 cm. Find the area enclosed by the pentagon ABECD.

Solution:

Question 16.
Polygon ABCDE is divided into parts as shown in the given figure. Find its area if AD = 8 cm, AH = 6 cm, AG = 4 cm, AF = 3 cm and perpendiculars BF = 2 cm, CH = 3 cm, EG = 2.5 cm.

Solution:

Question 17.
Find the area of polygon PQRSTU shown in 1 the given figure, if PS = 11 cm, PY = 9 cm, PX = 8 cm, PW = 5 cm, PV = 3 cm, QV = 5 cm, UW = 4 cm, RX = 6 cm, TY = 2 cm.

Solution:

## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.1

Question 1.
The length and breadth of a rectangular field are in the ratio 9 : 5. If the area of the field is 14580 square metres, find the cost of surrounding the field with a fence at the rate of ₹3·25 per metre.
Solution:

Question 2.
A rectangle is 16 m by 9 m. Find a side of the square whose area equals the area of the rectangle. By how much does the perimeter of the rectangle exceed the perimeter of the square?
Solution:

Question 3.
Two adjacent sides of a parallelogram are 24 cm and 18 cm. If the distance between longer sides is 12 cm, find the distance between shorter sides.
Solution:

Question 4.
Rajesh has a square plot with the measurement as shown in the given figure. He wants to construct a house in the middle of the plot. A garden is developed around the house. Find the total cost of developing a garden around the house at the rate of ₹50 per m2.

Solution:

Question 5.
A flooring tile has a shape of a parallelogram whose base is 18 cm and the corresponding height is 6 cm. How many such tiles are required to cover a floor of area 540 m2? (If required you can split the tiles in whatever way you want to fill up the comers).
Solution:

Question 6.
An ant is moving around a few food pieces of different shapes scattered on the floor. For which food piece would the ant have to take a longer round?

Solution:

Question 7.
In the adjoining figure, the area enclosed between the concentric circles is 770 cm2. If the radius of the outer circle is 21 cm, calculate the radius of the inner circle.

Solution:

Question 8.
A copper wire when bent in the form of a square encloses an area of 121 cm2. If the same wire is bent into the form of a circle, find the area of the circle.
Solution:

Question 9.
From the given figure, find
(i) the area of ∆ ABC
(ii) length of BC
(iii) the length of altitude from A to BC

Solution:

Question 10.
A rectangular garden 80 m by 40 m is divided into four equal parts by two cross-paths 2.5 m wide. Find
(i) the area of the cross-paths.
(ii) the area of the unshaded portion.

Solution:

Question 11.
In the given figure, ABCD is a rectangle. Find the area of the shaded region.

Solution:

Question 12.
In the adjoining figure, ABCD is a square grassy lawn of area 729 m2. A path of uniform width runs all around it. If the area of the path is 295 m2, find
(i) the length of the boundary of the square field enclosing the lawn and the path.
(ii) the width of the path.

Solution: