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A solid sphere of radius 9 cm is melted to form a sphere of radius 6 cm and a right circular cylinder of same radius. The height of the cylinder so formed is
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- 19 cm
- 21 cm
- 23 cm
- 25 cm
- 19 cm
Correct Option: A
| Volume of larger sphere = | πR³ = | π(9)³ cu.cm. | ||
| 3 | 3 |
= 972π cu.cm.
| Volume of smaller sphere = | π(6)³ = 288π cu.cm. | |
| 3 |
Volume of cylinder = πr²h
= π × 36h = 36ph cu.cm.
∴ 288π + 36π h = 972π
⇒ 288 + 36h = 972
⇒ 36h = 972 – 288 = 684
| ⇒ h = | = 19 cm. | |
| 36 |
