JEE Main · 2006 · 30 Apr 2006 · Offline · Solid State

A face-centred cubic cell contains four atoms, counted as eight corner atoms shared one-eighth each plus six face atoms shared one-half each, $8\times \frac{1}{8}+6\times \frac{1}{2}=4$. Treating each atom as a sphere of volume $\frac{4}{3}\pi r^3$, the total volume of the atoms in the cell is $4\times \frac{4}{3}\pi r^3=\frac{16}{3}\pi r^3$.