A sphere and a cube have the same surface area. The ratio

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A sphere and a cube have the same surface area. The ratio of the volume of the sphere to that of the cube is ?

1. 1 : 2
2. √6 : √π
3. 6 : π
4. 3 : 1

Correct Option: B

Let r be the radius of the sphere and a be the side of the cube
∴ 4π r² = 6a²
r = √6 a / 2√π
⇒ r³ = 6√6a³ / 8π√π
⇒ Ratio of volume = (4/3 πr³)/a³
∴ Required ratio = √6 / √π