The fraction of volume occupied in a primitive cubic unit cell is

$$\begin{gathered} f=(4/3)\pi r^3/a^3 \\ =(4/3)\pi (a/2{)}^3/a^3 \\ =\pi /6=0.52 \end{gathered}$$.

The volume of a constituent Vi divided by the total volume of the mixture $V_i$ prior to mixing is known as the volume fraction