Question

The side length, d, of a cube that contains a sphere depends on the radius, r, of a sphere. Assuming that the faces of the cube are tangent to the sphere, write the volume of the cube as a function of the radius of the sphere.

Answer 1

naturally, the radius of the sphere is half the cube side, or d/2. So, d = 2r.

so, v = d^3 = 8r^3