Answer: 68%

The atoms in a simple cubic crystal are located at the corners of the units cell, a cube with side $a$.

Note: In this type of structure, total number of atoms is 2.

For a body centric cube, the radius = $\large\frac{\sqrt 3 a }{4}$

Packing Density $ = \large\frac{\text{Volume of atoms}}{\text{Volume of unit cell}}$

Volume of atoms $ =2 \large\frac{4}{3}$$\pi r^3$ and Volume of unit cell $= a^3$

Substituting $r = \large\frac{\sqrt 3 a }{4}$, we get:

Packing Density $ = \Large \frac{ 2\frac{4\pi}{3} (\frac{\sqrt 3 a }{4})^3}{a^3}$$ = \large\frac{\pi \sqrt 3}{8}$$ = 0.68$