Balbharti Maharashtra State Board Class 8 Maths Solutions covers the Practice Set 16.1 8th Std Maths Answers Solutions Chapter 16 Surface Area and Volume.
Surface Area and Volume Class 8 Maths Chapter 16 Practice Set 16.1 Solutions Maharashtra Board
Std 8 Maths Practice Set 16.1 Chapter 16 Solutions Answers
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
∴ \(\frac { 150 }{ 50 }=h\)
∴ 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.
∴ \(\text { Number of bricks }=\frac{\text { volume of the wall }}{\text { volume of a brick }}\)
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
iii. \(\text { Number of bricks }=\frac{\text { volume of the wall }}{\text { volume of a brick }}\)
= \(\frac{600 \times 50 \times 250}{25 \times 15 \times 10}\)
= 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
= \(\frac{18,00,00,000}{1000}\)
…[∵ 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.