Discussion
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- Question
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
- 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.
- 1. 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
- 2. 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
- 3. 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
- 4. 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
- 5. 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
- 6. 8988 ÷ 8 ÷ 4 =?
Options- A. 4494
- B. 561.75
- C. 2247
- D. 280.875
- E. None of these Discuss
- 7. 5358 x 51 =?
Options- A. 273258
- B. 273268
- C. 273348
- D. 273358 Discuss
- 8. The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number?
Options- A. 240
- B. 270
- C. 295
- D. 360 Discuss
- 9. 1397 x 1397 =?
Options- A. 1951609
- B. 1981709
- C. 18362619
- D. 2031719
- E. None of these Discuss
- 10. {(476 + 424)2 - 4 x 476 x 424} =?
Options- A. 2906
- B. 3116
- C. 2704
- D. 2904
- E. None of these Discuss
Volume and Surface Area problems
Search Results
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: 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: 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: 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: 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: 280.875
Explanation:
| Given Exp. = 8988 x | 1 | x | 1 | = | 2247 | = 280.875 |
| 8 | 4 | 8 |
Correct Answer: 273258
Explanation:
| 5358 x 51 | = 5358 x (50 + 1) |
| = 5358 x 50 + 5358 x 1 | |
| = 267900 + 5358 | |
| = 273258. |
Correct Answer: 270
Explanation:
Let the smaller number be x . Then larger number = ( x + 1365).
∴ x + 1365 = 6x + 15
⟹ 5x = 1350
⟹ x = 270
∴Smaller number = 270.
Correct Answer: 1951609
Explanation:
| 1397 x 1397 | = (1397)2 |
| = (1400 - 3)2 | |
| = (1400)2 + (3)2 - (2 x 1400 x 3) | |
| = 1960000 + 9 - 8400 | |
| = 1960009 - 8400 | |
| = 1951609. |
Correct Answer: 2704
Explanation:
| Given Exp. | = [(a + b)2 - 4ab], where a = 476 and b = 424 |
| = [(476 + 424)2 - 4 x 476 x 424] | |
| = [(900)2 - 807296] | |
| = 810000 - 807296 | |
| = 2704. |
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