Question

A hollow sphere sits snugly in a foam cube so that the sphere touches each side of the cube. In 1~3 sentences, describe how to find the volume of the foam.

Answer 1

To find the volume of the foam cube surrounding the hollow sphere, first calculate the volume of the cube using the formula \( V_{\text{cube}} = s^3 \), where \( s \) is the length of a side of the cube, which is equal to the diameter of the sphere. Next, calculate the volume of the hollow sphere using the formula \( V_{\text{sphere}} = \frac{4}{3} \pi r^3 \), where \( r \) is the radius of the sphere. Finally, subtract the volume of the sphere from the volume of the cube to find the volume of the foam: \( V_{\text{foam}} = V_{\text{cube}} - V_{\text{sphere}} \).