A body centred cubic lattice is made up of hollow sphere of B....

Effective number of atoms of B present in a unit cell = 2

Total volume of B unoccupied by A in a unit cell

$= 2 \times \dfrac{4}{3} \left(R^{3} - r^{3}\right) \times \pi$

$= \dfrac{7}{3} \pi R^{3}~ \left(\text{r} = \dfrac{\text{R}}{2}\right)<br /><br />Volume of unit cell = a³<br /><br />${\left(\dfrac{4 \text{R}}{\sqrt{3}}\right)}^{3} =\dfrac{6 4}{3 \sqrt{3}}$R^{3} \left(\sqrt{3} \text{a} = 4 \text{R}\right)$

Ratio of total volume of sphere B unoccupied by A in unit cell and volume of unit cell $= \dfrac{7 / 3 \pi R^{3}}{\dfrac{6 4}{3 \sqrt{3}} R^{3}} = \dfrac{7 \pi \sqrt{3}}{6 4}$