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A cube and a sphere have equal surface areas. Find the ratio of their volumes.
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- π : √6
- √π : √6
- √π : 6
- None of these
- π : √6
Correct Option: B
Let the edge of cube be x units and radius of sphere be y units.
∴ Surface area of cube = surface area of sphere
⇒ 6x² = 4πy²
| ⇒ | = | = | |||
| y² | 6 | 3 |
| ⇒ | = √ | ⇒ x : y = √2π : √3 | ||
| y | 3 |
2⇒ Volume of cube : Volume of sphere
| = x³ : | πy³ = 3x³ : 4πy³ | |
| 3 |
= 3 × 2π√2π : 4π × 3 × √3
= π√2π : 2√3
= √π : √6
