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A solid sphere of diameter 6 cms is melted and shaped as a hollow cylinder of outer radius 5 cms and height 4 cms. What is the thickness of the cylinder ?
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- 2 cm
- 2.5 cm
- 9 cm
- 1 cm
- 2 cm
Correct Option: D
| Volume of sphere = | πr³ = | π × (3)³ cu.cm. | ||
| 3 | 3 |
Let the thickness of cylinder be x cm.
∴ Its internal radius = (5 – x) cm
Now,
| volume of cylinder = | π × 27 | |
| 3 |
⇒ π{(5)² – (5 – x)²} × 4
| = | π × 27 | |
| 3 |
⇒ 25 – (25 + x² – 10x) = 9
⇒ x² – 10x + 9 = 0
⇒ x² – 9x – x + 9 = 0
⇒ x (x – 9) – 1 (x – 9) = 0
⇒ (x – 1) (x – 9) = 0
⇒ x = 1 because x ≠ 9
