Volume and Surface Area problems
- 1. 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
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 |
- 2. 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
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.
- 3. 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
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 |
- 4. 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
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.
- 5. 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
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.
- 6. The volume of a cube is 512 cm 3, Its surface area is?
Options- A. 64 cm2
- B. 256 cm2
- C. 384 cm2
- D. 512 cm2 Discuss
Correct Answer: 384 cm2
Explanation:
? a3 = 512 = 8 x 8 x 8
? a = 8 cm
? Surface area = 6a2
=[6 x (8)2] cm2
=384 cm2
- 7. The surface area of a cube is 726 m 2. Its volume is?
Options- A. 1300 m3
- B. 1331 m3
- C. 1452 m3
- D. 1542 m3 Discuss
Correct Answer: 1331 m3
Explanation:
Surface area = 6a2 = 726
? a2 = 121
? a = 11 cm
? Volume of the cube = (11 x 11 x 11) cm3
= 1331 cm3
- 8. If each side of a cube is doubled, then its volume? .
Options- A. Is doubled
- B. Becomes 4 times
- C. Becomes 6 times
- D. Becomes 8 times Discuss
Correct Answer: Becomes 8 times
Explanation:
Let the edge of original cube = x cm
Edge of new cube = (2x) cm
Ratio of their volumes = x3 : (2x)3
= x3 : 8x3
= 1 :8
Thus the volumes be comes 8 times.
- 9. Three metal cubes of sides 5 cm, 4 cm and 3 cm are melted and recast into a new cube. The length of the edge of this cube, is?
Options- A. 6 cm
- B. 8 cm
- C. 10 cm
- D. None of these Discuss
Correct Answer: 6 cm
Explanation:
Volume of new cube = (5)3 + (4)3 + (3)3 cm3
= 126 cm3
Edge of this cube = (6 x 6 x 6)1/3 = 6 cm
- 10. If the volumes of two cubes are in the ratio 8 : 1, the ratio of their edges, is?
Options- A. 8 : 1
- B. 2?2 : 1
- C. 2 : 1
- D. None of these Discuss
Correct Answer: 8 : 1
Explanation:
Volume of new cube = [(5)3 + (4)3 + (3)3] cm3
= 216 cm3
Edge of this cube = ( 6 x 6 x 6)1/3 = 6 cm
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