Given that $(1)$ the equation for the atomic packing factor is$,$ APF$=\frac{V_S}{V_C},(2)$ the volume of a

sphere is equal to $(\frac{4}{3})R^3,$ and $(3)$ the volume of a cube is equal to $a^3,$ answer the question

listed below. Hint: The edge length can be found in terms of $R$ using the Pythagorean

theorem.

The atomic packing factor $($APF$)$ of a BCC unit cell is equal to