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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.

A cube inscribed in a sphere with centre O. A line segment from the centre O to a vertex of the cube has length 6.

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 \(O\).