The area of the ring between two concentric circles, whose circumference are 88 cm and 132 cm, is

$$\begin{gathered} \text{ Circumference of Bigger circle }=132\mathrm{cm} \\ \begin{array}{l}2\mathrm{\pi R}=132\\ 2\times \frac{22}{7}\times \mathrm{R}=132\\ \mathrm{R}=\frac{132\times 7}{2\times 22}\\ \mathrm{R}=21\mathrm{cm} \\ \text{ Circumference of Smaller circle }=88\mathrm{cm} \\ \begin{array}{l}2\mathrm{\pi r}=88\\ 2\times \frac{22}{7}\times \mathrm{r}=88\\ \mathrm{r}=\frac{88\times 7}{2\times 22}\\ \mathrm{r}=44\mathrm{cm}\end{array}\end{array} \end{gathered}$$
$$\begin{gathered} \text{ Area of the ring = Area of bigger circle }-\text{ Area of smaller circle } \\ \begin{array}{l}=\pi {\mathrm{R}}^2-\pi {\mathrm{r}}^2\\ =\pi \left({\mathrm{R}}^2-{\mathrm{r}}^2\right.\\ =\frac{22}{7}\left({21}^2-{14}^2\right.\\ =\frac{22}{7}\times 245\\ =770{\mathrm{cm}}^2\end{array} \end{gathered}$$