Which of the following expression is correct for packing fraction of NaCl if ${\mathrm{a}}^{-}$ ions from one face and one diagonal are removed?

• Correct answer
  A

  $\frac{\frac{13}{3}\mathrm{\pi }{\mathrm{r}}_{-}^3+\frac{16}{3}\mathrm{\pi }{\mathrm{r}}_{+}^3}{8({\mathrm{r}}_{+}+{\mathrm{r}}_{-}{)}^3}$
• B

  $\frac{\frac{13}{3}\mathrm{\pi }{\mathrm{r}}_{-}^3+\frac{4}{3}\mathrm{\pi }{\mathrm{r}}_{+}^3}{8({\mathrm{r}}_{+}+{\mathrm{r}}_{-}{)}^3}$
• C

  $\frac{\frac{16}{3}\mathrm{\pi }{\mathrm{r}}_{-}^3+\frac{13}{3}\mathrm{\pi }{\mathrm{r}}_{+}^3}{8({\mathrm{r}}_{+}+{\mathrm{r}}_{-}{)}^3}$
• D

  $\frac{\frac{4}{3}\mathrm{\pi }{\mathrm{r}}_{-}^3+\frac{13}{3}\mathrm{\pi }{\mathrm{r}}_{+}^3}{8({\mathrm{r}}_{+}+{\mathrm{r}}_{-}{)}^3}$

Hence, the correct answer is option: 'A'.