-
The radius of the base and height of a right circular cone are in the ratio 5 : 12. If the volume of the cone is
314 2 cm³ 7
, the slant height (in cm) of the cone will be
-
- 12
- 13
- 15
- 17
- 12
Correct Option: B
Let the radius of the base of the cone be 5x cm and its height be 12x cm.
| ∴ V = | πr²h | |
| 3 |
| = 314 | = | × | × 5x × 5x × 12x | |||
| 7 | 3 | 7 |
| ⇒ x³ = | = 1 | |
| 7 × 22 × 25 × 12 |
⇒ x = 1
∴ Slant height of the cone = √5² + 12² = √25 + 144 = √169 = 13 cm.
[Note : For a right circular cone, 5² + 12² = 13²]
