Answer
APF of BCC is 0.68
Work Step by Step
$APF={\text{volume of atomic unit cell}}/{\text{total unit cell volume}}$
$V_{s}=\frac{4}{3}\pi r^3$
As we know BCC has a total of 2 atoms:
$V_{s}=2\times\frac{4}{3}\pi r^3=\frac{8}{3}\pi r^3$
Thus:
$V_{c}=a^3={\frac{4}{\sqrt{3}}r}^3$
$V_{c}=\frac{64}{3\sqrt{3}}r^3$
APF =$\frac{\frac{8}{3}\pi r^3}{\frac{64}{3\sqrt{3}}r^3}=0.68$
