jmc

Question

A steel sphere with a 3-inch radius is made by removing metal from the corners of a cube that has the shortest possible side lengths. How many cubic inches are in the volume of the cube?

Accepted Answer

A sphere with a 3-inch radius has a 6-inch diameter and can be inscribed in a cube with at least side length 6. Thus the smallest possible cube has side length 6 and volume

6^{3} = 216

cubic inches.