Question

Find the area of the shaded portion in the adjoining figure

Answer 1

The area of circle of sector angle ${30}^{\circ }$ is equal to $\frac{1}{12}th$ of the entire circle which makes the angle of ${360}^{\circ }$.

Now the area of the shaded portion = Area of entire sector of the circle - Area of sector non-shaded.

$=\left[\frac{1}{12}\pi R^2\right]-\left[\frac{1}{12}\pi r^2\right]$

$=\frac{1}{12}\pi (R^2-r^2)$

$=\frac{1}{12}\times \frac{22}{7}\times ({42}^2-{21}^2)$

$=\frac{1}{12}\times \frac{22}{7}\times 1323$

$=346.5c{m}^2$