Question

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

Answer 1

Here's a crude picture of a cross section. Each edge of the cube has to be twice as long as the radius of the sphere. Then each face of the cube has area of (2r)^2 = 4r^2. And there are six faces to the cube . . .