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