Question

In the figure, find the area of the shaded region, enclosed between two concentric circles of radii $7cm$ and $14cm$ where$\angle AOC=40°$. Consider $\mathrm{\pi }=\frac{22}{7}$

Answer 1

Step 1: Given Data

Let $R$ is the outer radius of circle = $14cm$

Let $r$ is the inner radius of circle = $7cm$

Here $\theta =40°$

Step 2: Calculate area of shaded region

$\therefore$Area of shaded region is

$$\begin{gathered} =\frac{360°-\theta }{360°}\times \mathrm{\pi }\left({\mathrm{R}}^2-{\mathrm{r}}^2\right) \\ =\frac{360°-40}{360°}\times \mathrm{\pi }\left({\left(14\right)}^2-{\left(7\right)}^2\right) \\ =\frac{320°}{360°}\times \mathrm{\pi }\left({\left(14\right)}^2-{\left(7\right)}^2\right) \\ =\frac{8}{9}\times \frac{22}{7}\left(196-49\right)=\frac{8}{9}\times \frac{22}{7}\times 147 \\ =\frac{1232}{3}=410.67{\mathrm{cm}}^2 \end{gathered}$$

Hence the required area of region is $410.67c{m}^2$