Radii of A⁺ and that of X^- and Y^- have been given as A⁺= 1.00 pm, X^- =1.00 pm, Y^- = 2.00 pm.
Thus, ratio of volumes of AX and AY unit cells is

Ratio of r₊/r_ will decide the type of unit cell.

For $\mathrm{AX}\frac{r_{A^{+}}}{r_{X^{-}}}=\frac{1}{1}=1.0$ hence, AX has bcc structure. 

$\begin{array}{l}\therefore 2\left(r_{A^{+}}+r_{X^{-}}\right)=a\sqrt{3}\\ \mathrm{a}=\frac{2}{\sqrt{3}}\left(r_{A^{+}}+r_{X^{-}}\right)\\ =2\times \frac{2}{\sqrt{3}}=\frac{4}{\sqrt{3}}\mathrm{PM}\end{array}$

$\begin{array}{l}\therefore \text{ Volume }\left(\mathrm{AX}\right)={\mathrm{a}}^3={\left(\frac{4}{\sqrt{3}}\right)}^3=\frac{64}{3\sqrt{3}}\\ \text{ For AY }\frac{r_{A^{+}}}{r_{Y^{-}}}=\frac{1}{2}=0.5\end{array}$

Thus, octahedral or square planar structure.

$r=\frac{a}{2}$

$$\begin{gathered} \therefore \mathrm{a}=2\mathrm{r}=2\left(r_{A^{+}}+r_{Y^{-}}\right)=2(1+2)=6\mathrm{pm} \\ \text{ Volume }\left(\mathrm{AY}\right)={\mathrm{a}}^3=216{\mathrm{pm}}^3 \\ \therefore \text{ Ratio }=\frac{\text{ Volume }\left(\mathrm{AX}\right)}{\text{ Volume }\left(\mathrm{AY}\right)}=\frac{64}{3\sqrt{3}\times 216}=0.057 \end{gathered}$$