Ionic radii of cation ${\mathrm{A}}^{+}$ and anion ${\mathrm{B}}^{-}$ are $102$ and $181\mathrm{pm}$ respectively. These ions are allowed to crystallize into an ionic solid. This crystal has cubic close packing for ${\mathrm{B}}^{-}.{\mathrm{A}}^{+}$ is present in all octahedral voids. The edge length of the unit cell of the crystal $\mathrm{AB}$ is___$\mathrm{pm}$.

In given ionic compound anions form CCP lattice, And cation is present in octahedral void. Means this structure is similar to structure of NaCl. Which is also called rock salt structure.

Edge length = $\mathrm{a}=?$

In rock salt structure cations and anions are in contact along the edge of the cube. 

So, $\mathrm{a}=2\left({\mathrm{r}}_{+}+{\mathrm{r}}_{-}\right)$

$\mathrm{a}=2\left(102+181\right)$

$\mathrm{a}=2\left(283\right)$

$\mathrm{a}=566 \mathrm{pm}$