Question

A sphere and a cube have equal surface areas . show that the ratio of the volume of a sphere to that of the cube is root 6 : root x.

Answer 1

Heya !!



Let the radius of the sphere be r and the edge or cube be a.




Then,


Surface area of the sphere = Surface Area of cube.



=> 4πr² = 6a²




=> a² = 2/3πr²



=> a = √2/3 πr²





Therefore,



Required Ratio = Volume of sphere : Volume of cube.



=> 4/3 πr³ : a³



=> 4/3πr³ : 2/3πr³ × √2π/3




=> 2 : √2π/3



=> √2 : √π/3




=> √6 : √π

Answer 2

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