Volume and Surface Area problems
- 1. A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
Options- A. 49 m2
- B. 50 m2
- C. 53.5 m2
- D. 55 m2 Discuss
Correct Answer: 49 m2
Explanation:
| Area of the wet surface | = [2(lb + bh + lh) - lb] |
| = 2(bh + lh) + lb | |
| = [2 (4 x 1.25 + 6 x 1.25) + 6 x 4] m2 | |
| = 49 m2. |
- 2. A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:
Options- A. 12 kg
- B. 60 kg
- C. 72 kg
- D. 96 kg Discuss
Correct Answer: 60 kg
Explanation:
| Volume of water displaced | = (3 x 2 x 0.01) m3 |
| = 0.06 m3. |
| ∴ Mass of man | = Volume of water displaced x Density of water |
| = (0.06 x 1000) kg | |
| = 60 kg. |
- 3. How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
Options- A. 5600
- B. 6000
- C. 6400
- D. 7200 Discuss
Correct Answer: 6400
Explanation:
| Number of bricks = | Volume of the wall | = | ❨ | 800 x 600 x 22.5 | ❩ | = 6400. |
| Volume of 1 brick | 25 x 11.25 x 6 |
- 4. A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:
Options- A. 12Π cm3
- B. 15Π cm3
- C. 16Π cm3
- D. 20Π cm3 Discuss
Correct Answer: 12Π cm3
Explanation:
Clearly, we have r = 3 cm and h = 4 cm.
| ∴ Volume = | 1 | Πr2h = | ❨ | 1 | x Π x 32 x 4 | ❩cm3 | = 12Π cm3. |
| 3 | 3 |
- 5. The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.
Options- A. 3 : 7
- B. 7 : 3
- C. 6 : 7
- D. 7 : 6 Discuss
Correct Answer: 7 : 3
Explanation:
| Πr2h | = | 924 | ⟹ r = | ❨ | 924 | x 2 | ❩ | = 7 m. |
| 2Πrh | 264 | 264 |
| And, 2Πrh = 264 ⟹ h = | ❨ | 264 x | 7 | x | 1 | x | 1 | ❩ | = 6m. |
| 22 | 2 | 7 |
| ∴ Required ratio = | 2r | = | 14 | = 7 : 3. |
| h | 6 |
- 6. What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?
Options- A. 344.35 cm2
- B. 462 cm2
- C. 498.35 cm2
- D. None of these Discuss
Correct Answer: 498.35 cm2
Explanation:
h = 14 cm, r = 7 cm.
So, l = √(7)2 + (14)2 = √245 = 7√5 cm.
| ∴ Total surface area | = Πrl + Πr2 | |||||||||
|
||||||||||
| = [154(√5 + 1)] cm2 | ||||||||||
| = (154 x 3.236) cm2 | ||||||||||
| = 498.35 cm2. |
- 7. 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be:
Options- A. 20 cm
- B. 25 cm
- C. 35 cm
- D. 50 cm Discuss
Correct Answer: 25 cm
Explanation:
Total volume of water displaced = (4 x 50) m 3 = 200 m 3 .
| ∴ Rise in water level = | ❨ | 200 | ❩m 0.25 m = 25 cm. |
| 40 x 20 |
- 8. 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:
Options- A. 84
- B. 90
- C. 168
- D. 336 Discuss
Correct Answer: 84
Explanation:
Let the length of the wire be h
| Radius = | 1 | mm | = | 1 | cm. | Then, |
| 2 | 20 |
| ⟹ | 22 | x | 1 | x | 1 | x h = 66. |
| 7 | 20 | 20 |
| ⟹ h = | ❨ | 66 x 20 x 20 x 7 | ❩ | = 8400 cm = 84 m. |
| 22 |
- 9. A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
Options- A. 720
- B. 900
- C. 1200
- D. 1800 Discuss
Correct Answer: 1200
Explanation:
2(15 + 12) x h = 2(15 x 12)
| ⟹ h = | 180 | m = | 20 | m. |
| 27 | 3 |
| ∴ Volume = | ❨ | 15 x 12 x | 20 | ❩m3 | = 1200 m3. |
| 3 |
- 10. A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:
Options- A. 90 cm
- B. 1 dm
- C. 1 m
- D. 1.1 cm Discuss
Correct Answer: 1 dm
Explanation:
Let the thickness of the bottom be x cm.
Then, [(330 - 10) x (260 - 10) x (110 - x)] = 8000 x 1000
⟹ 320 x 250 x (110 - x) = 8000 x 1000
| ⟹ (110 - x) = | 8000 x 1000 | = 100 |
| 320 x 250 |
⟹ x = 10 cm = 1 dm.
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