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Thousand solid metallic spheres of diameter 6 cm each are melted and recast into a new solid sphere. The diameter of the new sphere (in cm) is
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- 30
- 90
- 45
- 60
- 30
Correct Option: D
| Volume of each smaller sphere = | πr³ | |
| 3 |
| = | π × (3)³ = 36 &p; cu.cm. | |
| 3 |
If the radius of larger sphere be R cm, then
| πR³ = 1000 × 36π | ||
| 3 |
| ⇒ R³ = | |
| 4 |
= 1000 × 3 × 3 × 3
∴ R = ³√1000 × 3 × 3 × 3
= 10 × 3 = 30 cm.
∴ Its diameter = (2 × 30) cm. = 60 cm
