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

C is the length of the edges of the cube.
S = C/2 = the Radius of the sphere.

Now what?

Answer 2

The surface area of a cube is equal to 6 times the edge length squared. To find the edge length, consider that the distance from the center of the sphere to outside of the sphere is the radius, which is also the distance from the center of the cube to the center of any face of the cube, or half of the edge length.