The packing factor is defined as the ratio of the volume of atoms in a unit cell to the volume of the unit cell, calculated as:
\[\text{Packing Factor} = \frac{\text{Volume of atoms in a unit cell}}{\text{Volume of the unit cell}}\]
For Face-Centered Cubic (FCC) structures, the packing factor is determined to be:
\[\text{Packing Factor} = \frac{4 \times \frac{4}{3} \pi r^3}{a^3} = 0.74\]
where \(a = \frac{4r}{\sqrt{2}}\). This demonstrates that \(74\%\) of the unit cell's total volume is occupied by atoms.