What are the packing fraction $(P.F)$ of Diamond cubic and Hexagonal close packing

Diamond cubic $\left(DC\right)$

Radius of atom, $r=\frac{\sqrt{3}.a}{8};Z_{eff}=8$

$PF=\frac{8\times \frac{4}{3}\pi r^3}{a^3}=\frac{8\times \frac{4}{3}\pi {\left(\frac{\sqrt{3}.a}{8}\right)}^3}{a^3}=\frac{\sqrt{3}\pi }{16}=0.34$

$hcp;radiusofatomr=\frac{a}{2};z_{eff}=6$

$\begin{array}{l}height=4r\times \sqrt{\frac{2}{3}};Basearea=6\sqrt{3}.r^2\\ volumeofunitcell=24\sqrt{2}{r}^3\end{array}$

$\begin{array}{l}P.F=\frac{6\times \frac{4}{3}\pi r^3}{a^3}=\frac{6\times \frac{4}{3}\pi r^3}{24\sqrt{2}{r}^3}\\ =\frac{\pi }{3\sqrt{2}}=0.74\end{array}$