Problem of the Week

Problem E

All Around the Cube

A cube is said to be inscribed in a sphere when all the vertices of the cube are on the surface of the sphere. In the diagram below, the cube is inscribed in the sphere with centre $$O$$. If the radius of the sphere is 6 cm, determine the volume of the cube.

Note:
In solving the above problem, it may be helpful to use the fact that if a cube is inscribed in a sphere with centre $$O$$, then the cube will also have centre $$O$$.