The volume of the cube with the shortest possible side lengths is 216 cubic inches.
If 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, then the side lengths of the cube must be equal to the diameter of the sphere.
side length of cube = diameter of sphere
side length of cube = 2 x radius of sphere
side length of cube = 2 x 3 inches
side length of cube = 6 inches
The volume of the cube can be calculated using the formula below.
V = s³
where V = volume and s = side length of cube
V = (6 inches)³
V = 216 cubic inches
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