Let the side of the cube=a
So, the surface area of the cube=6a2
Let the radius of the sphere=r
So, the surface area of the sphere =4πr2
Therefore,
6a2=4πr2 =x(let)
Therefore,
a=√x6
And r=√x4π
Therefore, ratio of their volumes,
=a343πr3
=(√x6)343π(√x4π)3
=16√1643π14π√14π
=12√4π√6
=√4π24
=√π√6
So, the ratio is √π:√6.