## Fraction of Space Filled by Hexagonal Close Packing

$r$
$8 (\frac{4/3 \pi r^3}{8}) + \frac{4}{3} \pi r^3 = \frac{8}{3} \pi r^3$
$4r$
$a$
$a^2+a^2+a^2=(4r)^2 \rightarrow a = \sqrt{4r}{\sqrt{3}}$
$\frac{8/3 \pi r^3}{(4r/ \sqrt{3}})^3 =\frac{\pi \sqrt{3}}{8}$