A sphere is inscribed in a cube. What is the ratio of the volume of the cube to the volume of the sphere?

6 : π

We know that,

Volume of sphere = \(\frac{4}{3}\)πr³ 

Let, Side of cube = x

then, Volume of cube = x³

Radius of sphere r = \(\frac{x}{2}\)

Volume of sphere = \(\frac{4}{3}\) π × \(\frac{x}{2}\)³ = \(\frac{x^3}{6}\)π

Volume of cube : Volume of sphere = x³ : \(\frac{x^3}{6}\)π = 6 : π