Question

A sphere is contained inside of a cube, tangent to all six faces. Find the surface area of the cube as a function of the radius of the sphere.

The answer in the back of the book read:A=24r^2...How did they get this answer? Thanks for helping!

Answer 1

Say the radius of the sphere is r. The sphere touches both sides of the cube, so the distance between two faces of the cube is 2r. But that also equals one edge, so one side of the cube has area 2r x 2r = 4r². But a cube has six such sides...