1) For FCC, we know that, effective number of atoms/unit cell i.e. n=4.

2) Volume of 1 atom = $\dfrac {4}{3} \Pi r^{3} \\$ 3) Volume of 1 unit cell = $a^{3}=(2\sqrt{2}r)^{3}$ $\because a=2\sqrt{2}r$ 4) By definition – APF= $\dfrac {n\times volume\ of\ 1\ atom}{volume\ of\ unit\ cell} \$

$=\dfrac …