A) \[\frac{12}{3}\pi {{r}^{3}}\]
B) \[\frac{16}{3}\pi {{r}^{3}}\]
C) \[\frac{20}{3}\pi {{r}^{3}}\]
D) \[\frac{24}{3}\pi {{r}^{3}}\]
Correct Answer: B
Solution :
\[a=2\sqrt{2}r\] Volume of the cell \[={{a}^{3}}={{(2\sqrt{2}r)}^{3}}=16\sqrt{2}{{r}^{3}}\] No. of spheres in fcc\[~=8\times \frac{1}{8}+6\times \frac{1}{2}=4\] Volume of 4 spheres \[=4\times \frac{4}{3}\pi {{r}^{3}}=\frac{16}{3}\pi {{r}^{3}}\]
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