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A hollow hemispherical bowl is made of silver with its outer radius 8 cm and inner radius 4 cm respectively. The bowl is melted to form a solid right circular cone of radius 8 cm. The height of the cone formed is
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- 7 cm.
- 9 cm.
- 12 cm.
- 14 cm.
- 7 cm.
Correct Option: D
| Volume of the silver used in hollow hemispherical bowl = | π(R³ - r³)cu.cm. | |
| 3 |
Where R = external radius r = internal radius
| = | π(8³ - 4³)cu.cm. | |
| 3 |
| = | π(512 - 64)cu.cm. | |
| 3 |
| = | × 448 cu.cm. | |
| 3 |
| ∴ Volume of cone = | πr1²h | |
| 3 |
| = | π 8² × h | |
| 3 |
| ∴ | π 8² × h = | × 448 | ||
| 3 | 3 |
| ⇒ h = | = 14 cm. | |
| 8 × 8 |
