Explain the calculation of packing efficiency in $hcp$ and $ccp$ structures with the help of a diagram.

(N/A) In $\triangle EFD$,
$AC^2 = b^2 = BC^2 + AB^2 = a^2 + a^2 = 2a^2$
$b = \sqrt{2}a$
If $r$ is the radius of the sphere,then $b = 4r = \sqrt{2}a$,or $a = \frac{4r}{\sqrt{2}} = 2\sqrt{2}r$.
We know that in $ccp$ structure,each unit cell effectively contains $4$ spheres.
Total volume of four spheres = $4 \times \frac{4}{3} \pi r^3$.
Volume of the unit cell = $a^3 = (2\sqrt{2}r)^3 = 16\sqrt{2}r^3$.
Packing efficiency = $\frac{\text{Volume occupied by four spheres in the unit cell} \times 100}{\text{Total volume of the unit cell}} \%$
$= \frac{4 \times (4/3) \pi r^3 \times 100}{16\sqrt{2}r^3} \% = 74 \%$.