Question

Question 98

Find the area of the shaded region:

Answer 1

Let the radius of smaller circle be r and bigger circle be R.
From the figure, $r=\frac{7}{2}cmandR=\frac{7}{2}+7=\frac{21}{2}cm$
$\therefore$ Area of shaded region = Area of bigger circle - Area of smaller circle
$=\pi R^2-\pi r^2=\pi (R^2-r^2)=\pi (\frac{21}{2}\times \frac{21}{2}-\frac{7}{2}\times \frac{7}{2})$
$=\pi (\frac{441}{4}-\frac{49}{4})=\frac{22}{7}\times \frac{392}{4}=308c{m}^2$
Hence, the area of shaded region is $308c{m}^2.$