The packing efficiency in a face - centred cubic cell system of crystals is

Volume of four spheres is given by
 $V=4\times {\displaystyle \frac{4}{3}}\pi r^3$
In FCC, the corner spheres are in touch with the face centered sphere so the relation between the edge length and radius of the sphere is given by
$\mathrm{r}=\frac{\mathrm{a}}{4\sqrt{2}}$
 packing efficiency=volume occupied by all the spheres in unit cellTotal volume of the unit cell×100$\mathrm{packing}\mathrm{efficiency}=\frac{\mathrm{volume}\mathrm{occupied}\mathrm{by}\mathrm{all}\mathrm{the}\mathrm{spheres}\text{ in }\mathrm{unit}\mathrm{cell}}{\mathrm{Total}\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{unit}\mathrm{cell}}\times 100$

 
$Packingfraction={\displaystyle \frac{n\times {\displaystyle \frac{4}{3}}\pi r^3}{a^3}}$

Packing  fraction = $\frac{4\times {\displaystyle \frac{4}{3}}\times {\left({\displaystyle \frac{\mathrm{a}}{4\times \sqrt{2}}}\right)}^3}{{\mathrm{a}}^3}$

Packing fraction = $\frac{\mathrm{\pi }}{3\sqrt{2}}$ = 0.74