If the circumferences of two concentric circles forming a ring are 88 cm and 66 cm respectively. Find the width of the ring.

It is given that the circumferences of two concentric circles forming a ring are 88 cm and 66 cm respectively and we need to find the width of the ring.

It is given that the circumference of the larger circle having radius say r₁ is 88 cm. Therefore,

$\begin{array}{l}2{\mathrm{\pi r}}_1=88\\ \Rightarrow {\mathrm{r}}_1=14\mathrm{cm}\end{array}$

Similarly, the circumference of the smaller circle having radius say r2 is 66 cm. Therefore,

$\begin{array}{l}2{\mathrm{\pi r}}_2=66\\ \Rightarrow {\mathrm{r}}_2=10.5\mathrm{cm}\end{array}$

It is known that for two concentric circles, the width is equal to the difference in the radius of the circles. Mathematically,

$\mathrm{w}={\mathrm{r}}_1-{\mathrm{r}}_2$, where

w is the width,

r₁ is the radius of the larger circle and

r₂ is the radius of the smaller circle.

On substituting the given value, we get the width as

$\begin{array}{l}\Rightarrow \mathrm{w}={\mathrm{r}}_1-{\mathrm{r}}_2\\ \Rightarrow \mathrm{w}=14-10.5\\ \Rightarrow \mathrm{w}=3.5\end{array}$

Hence, the width of the ring is 3.5.