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Three small lead spheres of radii 3 cm, 4 cm and 5 cm respectively, are melted into a single sphere. The diameter of the new sphere is
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- 6 cm
- 7 cm
- 8 cm
- 12 cm
- 6 cm
Correct Option: D
| Volume of new single sphere = | π (r1³ + r2³ + r3³) | |
| 3 |
| = | π (3³ + 4³ + 5³) cu.cm. | |
| 3 |
| = | π (27 + 64 + 125) cu.cm. | |
| 3 |
| = | π × 216 cu.cm. | |
| 3 |
| ∴ | πR³ = | π × 216 | ||
| 3 | 3 |
where R = radius of new sphere
∴ R³ = 216
⇒ R = ³√216 = ³√6 × 6 × 6 = 6 cm
∴ Diameter of new sphere = 2 × 6 = 12
