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A large solid sphere is melted and moulded to form identical right circular cones with base radius and height same as the radius of the sphere. One of these cones is melted and moulded to form a smaller solid sphere. Then the ratio of the surface area of the smaller to the surface area of the larger sphere is
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- 1 : 34/3
- 1 : 2 ³/2
- 1 : 3 ²/3
- 1 : 2 4/3
- 1 : 34/3
Correct Option: D
Radius of larger sphere = R units
| ∴ Its volume = | πR³ cu. units | |
| 3 |
| Volume of smaller cone = | πR³ cu. units | |
| 3 |
| Volume of smaller sphere = | πR³ | |
| 3 |
| ∴ | πr³ = | πR³ | ||
| 3 | 3 |
| ⇒ r³ = | ||
| 4 |
| ⇒ r = | ||
| ³√4 |
∴ Surface area of smaller sphere : Surface area of larger sphere
= 4πr² : 4πR²
= r² : R²
| = |  |  | ² | : R² = 1 : (³√4)² | |
| ³√4 |
= 1 : [{(2²)}¹/3]³ = 1 : 24/3
