Total volume of all atoms present in face centred cubic unit cell of metal is (r = atomic radius)

$$\begin{gathered} {\mathrm{Z}}_{\mathrm{eff} } \mathrm{in} \mathrm{FCC} \mathrm{unit}\mathrm{cell} =6\times \frac{1}{2}+\frac{1}{8}\times 8 = 4 (\mathrm{no}.\mathrm{of} \mathrm{atoms} \mathrm{per} \mathrm{unit} \mathrm{cell}) \\ \text{ Volume of one atom }=\frac{4}{3}\pi r^3 \\ \text{ Volume of atoms in }\mathrm{FCC}=4\times \frac{4}{3}\pi {\mathrm{r}}^3 = =\frac{16}{3}{\mathrm{\pi r}}^3 \end{gathered}$$

Therefore, the correct option is D