Discussion
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- Question
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
- Correct Answer
- 25 : 18
Explanation
Volume of the large cube = (3 3 + 4 3 + 5 3 ) = 216 cm 3Let 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 - 1. 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
- 2. 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
- 3. 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
- 4. 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
- 5. 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
- 6. 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
- 7. In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
Options- A. 75 cu. m
- B. 750 cu. m
- C. 7500 cu. m
- D. 75000 cu. m Discuss
- 8. A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:
Options- A. 4830
- B. 5120
- C. 6420
- D. 8960 Discuss
- 9. The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.
Options- A. 30Π m2
- B. 40Π m2
- C. 60Π m2
- D. 80Π m2 Discuss
- 10. 8988 ÷ 8 ÷ 4 =?
Options- A. 4494
- B. 561.75
- C. 2247
- D. 280.875
- E. None of these Discuss
Volume and Surface Area problems
Search Results
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: 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: 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: 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 |
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: 3.696 kg
Explanation:
External radius = 4 cm,
Internal radius = 3 cm.
| Volume of iron |
|
||||||
|
|||||||
| = 462 cm3. |
∴ Weight of iron = (462 x 8) gm = 3696 gm = 3.696 kg.
Correct Answer: 750 cu. m
Explanation:
1 hectare = 10,000 m 2
So, Area = (1.5 x 10000) m2 = 15000 m2.
| Depth = | 5 | m | = | 1 | m. |
| 100 | 20 |
| ∴ Volume = (Area x Depth) = | ❨ | 15000 x | 1 | ❩m3 | = 750 m3. |
| 20 |
Correct Answer: 5120
Explanation:
Clearly, l = (48 - 16)m = 32 m,
b = (36 -16)m = 20 m,
h = 8 m.
∴ Volume of the box = (32 x 20 x 8) m3 = 5120 m3.
Correct Answer: 60Π m2
Explanation:
l = 10 m,
h = 8 m.
So, r = √l2 - h2 = √(10)2 - 82 = 6 m.
∴ Curved surface area = Πrl = (Π x 6 x 10) m2 = 60Π m2.
Correct Answer: 280.875
Explanation:
| Given Exp. = 8988 x | 1 | x | 1 | = | 2247 | = 280.875 |
| 8 | 4 | 8 |
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