Cube A is inscribed in sphere B, which is inscribed in cube C. If the sides of cube A have length 4, what is the volume of cube C?

Answer 1

When a cube is inscribed in a sphere, the long diagonal of the cube is a diameter of the sphere. So, the sphere has diameter 4√3

Similarly, the diameter of the sphere is equal to the side of cube C, so it has side 4√3.

so, ...

Answer 2

the volume of a sphere inscribed in a cube of diagonal 4√3 is