Question

A sphere fits inside a cube with the sphere's diameter equal to the width of the cube, 20 centimeters. What is the volume of the cube not filled by the sphere? The volume not filled by the sphere is approximately cm³

Answer 1

The volume of the cube not filled by the sphere is the difference between the total volume of the cube and the sphere. With this in mind let's calculate each of these volumes. First the volume of the cube.

`\begin{gathered} V_{\text{cube}}=width^3 \\ V_{\text{cube}}=20^3=8000\text{ cubic centimeters} \end{gathered}`

Then we need to calculate the volume of the sphere:

`\begin{gathered} V_{\text{sphere}}=(4)/(3)\pi\cdot r^3=(4)/(3)\cdot\pi\cdot((20)/(2))^3 \\ V_{\text{sphere}}=(4)/(3)\cdot\pi\cdot10^3=4186.67 \end{gathered}`

The volume of the cube not filled by the sphere is:

`V=V_{\text{cube}}-V_{\text{sphere}}=8000-4186.67=3813.33`

The volume is 3813.33 cubic centimeters