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In a simple cubic lattice, there is only one atom per unit cell, which has a volume of

 $\frac{4}{3}\pi r^3=\frac{4}{3}\pi {\left(\frac{a}{2}\right)}^3=\frac{\pi a^3}{6}$

The ratio of the volume of the atom to the volume of the unit cell is the fraction of the unit cell that is occupied, or the packing fraction. It is also called the atomic packing factor.