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If the radius of the base of a cone be 7 cm and its curved surface area be 550 sq. cm, then the volume of the cone is
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- 1232 cu. cm
- 1024 cu. cm
- 1132 cu. cm
- 1324 cu. cm
- 1232 cu. cm
Correct Option: A
Curved surface area of cone = 550 sq. cm.
⇒ πrl = 550
| ⇒ | × 7 × √r² + h² = 550 | |
| 7 |
| ⇒ | × 7 × √49 + h² = 550 | |
| 7 |
| ⇒ √49 + h² = | = 25 | |
| 22 |
⇒ 49 + h² = (25)² = 625
→ h² = 625 – 49 = 576
⇒ h = 576 = 24 cm.
| ∴ Volume of cone = | × | × 7 × 7 × 24 | |||
| 3 | 7 | ||||
= 1232 cu. cm.
