# DAV Class 8 Maths Chapter 14 Worksheet 5 Solutions

The DAV Maths Book Class 8 Solutions Pdf and DAV Class 8 Maths Chapter 14 Worksheet 5 Solutions of Mensuration offer comprehensive answers to textbook questions.

## DAV Class 8 Maths Ch 14 WS 5 Solutions

Question 1.
Two cubes each side 6 cm are joined together. Name the new solid formed and, also find its volume.
Solution:
The new solid formed is a cuboid whose length is 6 + 6 = 12 cm, breadth = 6 cm and height = 6 cm
∴ Volume of the cuboid = l × b × h
= 12 × 6 × 6
= 432 cm3

Question 2.
Find the height of a cuboid whose volume is 275 cm3 and the base area is 25 cm2.
Solution:
Base area lb = 25 cm2
Volume of the cuboid = l × b × h
⇒ 275 = 25 × h
⇒ h = $$\frac{275}{25}$$ = 11 cm
Hence, the required height = 11 cm

Question 3.
The dimensions of a box are 60 cm × 54 cm × 30 cm. How many small cubes of side 6 cm can be placed in the box?
Solution:
Volume of the box = 60 × 54 × 30 cm3
Volume of 1 small cube = 6 × 6 × 6 cm3
∴ Number of cubes that can be placed in the box = $$\frac{Volume of the box}{Volume of the small cube}$$
= $$\frac{60 \times 54 \times 30}{6 \times 6 \times 6}$$
= 450
Hence, the required number of cubes = 450

Question 4.
If each edge of a cube is doubled,
(i) How many times will its surface area increase?
(ii) How many times will its volume increase?
Solution:
Let the edge of a cube be l cm.
∴ Its surface area = 6l2 cm2 and its volume = l3 cm3
Now the edge of the cube = 2l cm
∴ Its surface area = 6(2l)2
= 6 × 4l2
= 24l2 cm
and its volume = (2l)3 = 8l3
(I) New surface area increased by original surface area = $$\frac{24 l^2}{6 l^2}$$ = 4 times
(ii) New volume increased by original volume = $$\frac{8 l^3}{l^3}$$ = 8 times.
Hence, (i) the surface area will increase 4 times and (ii) the volume will increase 8 times.

Question 5.
A matchbox measures 4 cm × 2.5 cm × 1.5 cm. What will be the volume of a packet containing 12 such boxes?
Solution:
Volume of one box = 4 × 2.5 × 1.5 cm = 15 cm3
∴ Volume of such 12 boxes = 12 × 15 = 180 cm3

Question 6.
The volume of a cube is 1000 cm3. Find its total surface area.
Solution:
Volume of cube = l3
⇒ l3 = 1000
⇒ l = $$(1000)^{1 / 3}$$ = 10 cm
The total surface area of the cube = 6l2
= 6 × 10 × 10
= 600 cm2

Question 7.
How many planks each of which is 2 m long, 2.5 cm broad, and 4 cm thick can be cut off from a wooden block 6 m long, 15 cm broad, and 40 cm thick?
Solution:
Length of the plank = 2 m
= 2 × 100
= 200 cm
breadth = 2.5 cm and height = 4 cm
∴ Its volume = l × b × h
= 200 × 2.5 × 4
= 2000 cm3
Now the length of the wooden block = 6 m
= 6 × 100
= 600 cm
breadth = 15 cm and height = 40 cm
∴ Its volume = 600 × 15 × 40 = 360000 cm3
∴ Number of planks = $$\frac{Volume of the block}{Volume of plank }$$
= $$\frac{360000}{2000}$$
= 180
Hence, the required number of planks = 180.

Question 8.
Three solid metal cubes with edges 6 cm, 8 cm, and 10 cm respectively are melted together and formed into a single cube. Find the volume of the new cube.
Solution:
Combined volume of the 3 cubes = (6)3 + (8)3 + (10)3
= 216 + 512 + 1000
= 1728 cm3
Hence, the volume of the new single cube = 1728 cm3

Question 9.
Find the volume of a cube whose surface area is 150 m2.
Solution:
∴ Surface area of a cube = 6l2
⇒ 6l2 = 150
⇒ l2 = 25
⇒ l = 5 m
∴ The volume of the cube = l3
= (5)3
= 125 m3

Question 10.
Find the volume of a cube, one face of which has an area of 81 m2.
Solution:
Area of each face of a cube = l2 m
⇒ l2 = 81
⇒ l = 9 m
∴ The volume of the cube = l3
= (9)3
= 729 m3