Answer: 74%
The atoms in a simple cubic crystal are located at the corners of the units cell, a cube with side $a$.
For a face centric cube, the radius = $\large\frac{\sqrt 2 a }{4}$
Note: In this type of structure, total number of atoms is 4 per unit cell.
Packing Density $ = \large\frac{\text{Volume of atoms}}{\text{Volume of unit cell}}$
Volume of atoms $ =4 \large\frac{4}{3}$$\pi r^3$ and Volume of unit cell $= a^3$
Substituting $r = \large\frac{\sqrt 2 a }{4}$, we get:
Packing Density $ = \Large \frac{ 4 \frac{4\pi}{3} (\frac{\sqrt 2 a }{4})^3}{a^3}$$ = \large\frac{\pi \sqrt 2}{6}$$ = 0.74$