Question

The areas of two concentric circles are 962.5 cm² and 1386 cm². Find the width of the ring.

Answer 1

Let the radii of the bigger and smaller circles be R cm and r cm, respectively.

Now,
Area of the bigger circle = $1386{\mathrm{cm}}^2$
Area = $\mathrm{\pi }{R}^2$
$$\begin{gathered} \Rightarrow 1386=\frac{22}{7}\times R^2 \\ \Rightarrow \frac{1386\times 7}{22}=R^2 \\ \Rightarrow R^2=441 \\ \Rightarrow R=21 \end{gathered}$$

Area of the smaller circle = $962.5{\mathrm{cm}}^2$
Area = $\mathrm{\pi }{r}^2$
$$\begin{gathered} \Rightarrow 962.5=\frac{22}{7}{r}^2 \\ \Rightarrow r^2=\frac{962.5\times 7}{22} \\ \Rightarrow r^2=306.25 \\ \Rightarrow r=17.5 \end{gathered}$$

∴ Width of the ring = R $-$ r
$$\begin{gathered} =21-17.5 \\ =3.5\mathrm{cm} \end{gathered}$$