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The diameters of the internal and external surfaces of a hollow spherical shell are 6 cm and 10 cm respectively. If it is melted and a solid cylinder of length 8/3 cm is made, then the diameter (in cm) of the cylinder is
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- 10
- 14
- 16
- 7
- 10
Correct Option: B
Volume of the material of the hollow cylinder
| = | π(R² - r²) | |
| 3 |
| = | π(5² - 3²) | |
| 3 |
| = | π(125 - 27) | |
| 3 |
| = | π cu.cm. | |
| 3 |
If the radius of the cylinder be R cm, then
| πR² × | = | ||
| 3 | 3 |
| ⇒ R² = | = 49 | |
| 8 |
⇒ R = √49 = 7 cm.
∴ Diameter = 2R = 2 × 7 = 14 cm.
