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The ratio of height and the diameter of a right circular cone is 3 : 2 and its volumeis 1078 cc, then (taking π = 22/7) its height is :
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- 7 cm
- 14 cm
- 21 cm
- 28 cm
- 7 cm
Correct Option: C
Let, Height of the cone = 3x cm and diameter = 2x cm.
∴ Radius = x cm.
| Volume = | πr²h | |
| 3 |
| ⇒ 1078 = | × | × x² × 3x | ||
| 3 | 7 |
| ⇒ 1078 = | x³ | |
| 7 |
| ⇒ x³ = | = 343 | |
| 22 |
⇒ x = 3√343 = 7
∴ Height = 3 × 7 = 21 cm
