S.chand Class 8 Maths Solution Chapter 17 Volume and Surface Area of Solids Exercise 17 B

 Exercise 17 B

Question 1

1. Work out the volume of each cuboid.

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2. Find the volume of each of the following cuboids:

	Length	Breadth	Height
(a)	5 cm	5 cm	4 cm
(b)	45 mm	30 mm	10 mm
(c)	12 cm	1.2 cm	0.5 cm
(d)	1.2 m	0.9 m	0.7 cm

3. Complete the table: Measurements are in cm

	(i)	(ii)	(iii)	(iv)	(v)	(vi)
Length	4	12	16	?	40	60
Breadth	3	9	14	28	24	?
Height	5	12	18	24	?	5
Volume	?	?	?	26208	2400	5400

4. Find the volume of a cube with the given side :

(a) $3 \mathrm{~cm}$

(b) $\frac{1}{5} \mathrm{~cm}$

(c) $1.2 \mathrm{~m}$

(d) $2.5 \mathrm{~m}$

5. Find each edge of the cubes whose volumes are :

(a) $216 \mathrm{~m}^{3}$

(b) $512 \mathrm{~cm}^{3}$

(c) $1728 \mathrm{~cm}^{3}$

(d) $2197 \mathrm{~m}^{3}$

6. Find the volume of air in a room measuring $4 \mathrm{~m}$ by $5 \mathrm{~m}$ which is $3 \mathrm{~m}$ high.

7. Which has the greater volume : a box that measures $10 \mathrm{~cm}$ by $6 \mathrm{~cm}$ by $4 \mathrm{~cm}$ or one that measures $6 \mathrm{~cm}$ by $6 \mathrm{~cm}$ by $7 \mathrm{~cm}$ ?

8. The bottom of a tank measures $25 \mathrm{~m} \times 20 \mathrm{~m}$. Find its depth if it contains $2000 \mathrm{~m}^{3}$ water.

9. Find the volume of a cube, one face of which has an area of $64 \mathrm{~cm}^{2}$.

10. A heap of wood is a pile $5 \mathrm{dm}$ wide, $9 \mathrm{dm}$ long, and $3 \mathrm{dm}$ high. What is the volume of the heap of wood?

11. The volume of a soap cake is $160 \mathrm{~cm}^{3}$. Its length and width are $10 \mathrm{~cm}$ and $5 \mathrm{~cm}$. Find its height.

12. If $60 \mathrm{~cm}^{3}$ of a metal weighs $1 \mathrm{~kg}$, find the weight of a block of the same metal of the size $20 \mathrm{~cm}$ by 12 cm by $5 \mathrm{~cm}$.

13. In a shower, $5 \mathrm{~cm}$ of rain falls. Find the volume of water that falls on 2 hectares of land.

14. A river 2 metres deep and 45 metres wide is flowing at the rate of $3 \mathrm{~km}$ per hour. Find the amount of water that runs into the sea per minute.

15. A beam $9 \mathrm{~m}$ long, $50 \mathrm{~cm}$ wide, and $20 \mathrm{~cm}$ deep is made of wood which weighs $30 \mathrm{~kg}$ per $\mathrm{m}^{3}$, find the weight of the beam.

16. A wooden box (including the lid) has external dimensions of $40 \mathrm{~cm}$ by $34 \mathrm{~cm}$ by $30 \mathrm{~cm}$. If the wood is $1 \mathrm{~cm}$ thick, how many $\mathrm{cm}^{3}$ of wood are there in it?

17. The outer dimensions of a closed wooden box are $10 \mathrm{~cm}$ by $8 \mathrm{~cm}$ by $7 \mathrm{~cm}$. Thickness of the wood is 1 $\mathrm{cm}$. Find the total cost of wood required to make the box if $1 \mathrm{~cm}^{3}$ of wood costs $₹ 2.00$.

18. 500 men took dip in a tank which is $80 \mathrm{~m}$ long, $50 \mathrm{~m}$ broad. What is the rise in water level if the average displacement of water by a man is $4 \mathrm{~m}^{3}$ ?

[Hint. Volume of water displaced by 500 men $=(4 \times 500)=2000 \mathrm{~m}^{3}$

Area of the tank $=80 \times 50=4000 \mathrm{~m}^{2}$. Let the rise in the level of water $=h$ metres. Then $4000 \times h=2000$ ]

Multiple Choice Questions (MCQs)

19. The three co-terminous edges of a cuboid are 36,75 and $80 \mathrm{~cm}$ respectively. The edge of the cube of the same volume will be :

(a) $60 \mathrm{~cm}$

(b) $55 \mathrm{~cm}$

(c) $50 \mathrm{~cm}$

(d) $65 \mathrm{~cm}$

20. If the volume of a cube is $729 \mathrm{~cm}^{3}$, then its surface area will be

(a) $486 \mathrm{~cm}^{2}$

(b) $476 \mathrm{~cm}^{2}$

(c) $466 \mathrm{~cm}^{2}$

(d) $456 \mathrm{~cm}^{2}$