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If the area of the base of a cone is 770 cm² and the area of the curved surface is 814 cm², then its volume (in cm³) is :
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- 213√5
- 392√5
- 550√5
- 616√5
- 213√5
Correct Option: D
Area of the base of cone = 770 cm²
⇒ r² = 770
| ⇒ | r = 770 | |
| 7 |
| ⇒ r² = | = 245 | |
| 22 |
∴ r = √245 = 7√5 cm
Curved surface area of the cone = πrl = 814
| ⇒ r = | × 7√5 × l = 814 | |
| 7 |
| ⇒ l = | = | cm. | ||
| 22 × √5 | √5 |
Let the height of the cone be h cm, then h² + r² = l²
| ⇒ h² + (7√5)² = |  |  | ² | |
| √5 |
| ⇒ h² + 245 = | ||
| 5 |
| ⇒ h² = | - 245 | |
| 5 |
| ⇒ h² = | = | ||
| 5 | 5 |
| ⇒ h = | cm | |
| √5 |
| ∴ Volume of the cone = | πr²h | |
| 3 |
| = | × | × 7√5 × 7√5 × | |||
| 3 | 7 | √5 |
= 616√5 cm&Sup3;
