Question

A sphere fits exactly into a cube. What is the ratio of the surface area of the sphere to the surface area of the cube?

Answer 1

Suppose the cube has a side 'a'. Then the sphere has a diameter 'a', hence radius 'a/2'. Now simply use the formulas for surface area of the two solids.

For cube it is 6a^2 and for sphere it is 4 pi r^2.