Discussion
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- Question
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
- 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 - 1. 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
- 2. 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
- 3. 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
- 4. 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
- 5. 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
- 6. 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
- 7. 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
- 8. 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
- 9. A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?
Options- A. 2 : 1
- B. 3 : 2
- C. 25 : 18
- D. 27 : 20 Discuss
- 10. A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3, then the weight of the pipe is:
Options- A. 3.6 kg
- B. 3.696 kg
- C. 36 kg
- D. 36.9 kg Discuss
Volume and Surface Area problems
Search Results
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. |
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 |
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 |
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 |
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. |
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 |
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 |
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.
Correct Answer: 25 : 18
Explanation:
Volume of the large cube = (3 3 + 4 3 + 5 3 ) = 216 cm 3
Let the edge of the large cube be a.
So, a3 = 216 ⟹ a = 6 cm.
| ∴ Required ratio = | ❨ | 6 x (32 + 42 + 52) | ❩ | = | 50 | = 25 : 18. |
| 6 x 62 | 36 |
Correct Answer: 3.696 kg
Explanation:
External radius = 4 cm,
Internal radius = 3 cm.
| Volume of iron |
|
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|
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| = 462 cm3. |
∴ Weight of iron = (462 x 8) gm = 3696 gm = 3.696 kg.
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