## Chapter 16 Surface Area and Volume Set 16.1

Question 1.

Find the volume of a box if its length, breadth and height are 20 cm, 10.5 cm and 8 cm respectively.

Given: For cuboid shaped box,

length (l) = 20 cm, breadth (b) = 10.5 cm and height (h) = 8cm

To find: Volume of a box

Solution:

Volume of a box = l x b x h

= 20 x 10.5 x 8

= 1680 cc

∴ The volume of the box is 1680 cc.

Question 2.

A cuboid shaped soap bar has volume 150 cc. Find its thickness if its length is 10 cm and breadth is 5 cm.

Given: For cuboid shaped soap bar,

length (l) = 10 cm, breadth (b) = 5 cm and volume = 150 cc

To find: Thickness of the soap bar (h)

Solution:

Volume of soap bar = l x b x h

∴ 150 = 10 x 5 x h

∴ 150 = 50h

∴ 150/50=*h*

∴ 3 = h

i.e., h = 3 cm

∴ The thickness of the soap bar is 3 cm.

Question 3.

How many bricks of length 25 cm, breadth 15 cm and height 10 cm are required to build a wall of length 6 m, height 2.5 m and breadth 0.5 m?

Given: For the cuboidal shape brick:

length (l_{1}) = 25 cm,

breadth (b_{1}) = 15 cm,

height (h_{1}) = 10 cm

For the cuboidal shape wall:

length (l_{2}) = 6 m,

height (h_{2}) = 2.5 m,

breadth (b_{2}) = 0.5 m

To find: Number of bricks required

Solution:

When all the bricks are arranged to build a wall, the volume of all the bricks is equal to volume of wall.

i. Volume of a brick = l_{1} x b_{1} x h_{1}

= 25 x 15 x 10 cc

ii. l_{2} = 6m = 6 x 100 …[∵ 1m = 100cm]

= 600 cm

h_{2} = 2.5 m = 2.5 x 100 = 250 cm

b_{2} = 0.5 m = 0.5 x 100 = 50 cm

Volume of the wall = l_{2} x b_{2} x h_{2}

= 600 x 50 x 250 cc

= 40 x 2 x 25

= 2000 bricks

∴ 2000 bricks are required to build the wall.

Question 4.

For rain water harvesting a tank of length 10 m, breadth 6 m and depth 3 m is built. What is the capacity of the tank? How many litre of water can it hold?

Given: For a cuboidal tank,

Length (l) = 10 m, breadth (b) = 6 m, depth (h) = 3 m

To find: Capacity of the tank and litre of water tank can hold.

Solution:

i. l = 10m = 10 x 100 …[∵ 1m = 100cm]

= 1000 cm,

b = 6 m = 6 x 100 = 600 cm,

h = 3 m = 3 x 100 = 300 cm

Volume of the tank = l x b x h

= 1000 x 600 x 300

= 18,00,00,000 cc

ii. Capacity of the tank = Volume of the tank

= 18,00,00,000 cc

…[∵ 1 litre =1000 cc]

= 1,80,000 litre

∴ The capacity of the tank is 18,00,00,000 cc and it can hold 1,80,000 litre of water.