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A solid metallic sphere of radius 8 cm is melted to form 64 equal small solid spheres. The ratio of the surface area of this sphere to that of a small sphere is
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- 4 : 1
- 1 : 16
- 16 : 1
- 1 : 4
- 4 : 1
Correct Option: C
| Volume of the solid metallicsphere = | πr³ | |
| 3 |
| = | × π × (8)³ | |
| 3 |
| = | π cm³ | |
| 3 |
Let the radius of the each small sphere be x cm
| ∴ 64 × | πx³ = | π | ||
| 3 | 3 |
| ⇒ x³ = | = 8 | |
| 64 × 4 |
⇒ x = ³√8 = 2cm
∴ Required ratio = 4π. (8)² : 4π (2)² = 64 : 4 = 16 : 1
