Question

In the given figure, $AB$ is the diameter of a circle with centre $O$ and $OA=7$ cm. Find the area of the shaded region

• A. $66.5$ sq. cm
• B. $62.5$ sq. cm
• C. $64.5$ sq. cm
• D. $69.5$ sq. cm

Answer 1

The correct option is A $66.5$ sq. cm

Area of smaller circle$=r^2=x(3.5{)}^2=38.5$ sq cm
Area of bigger circle $=4\times 38.5$ (because radius is double that of smaller circle)
Hence, area of bigger semicircle $=2\times 38.5=77$ sq cm
Area of $ABC=\frac{1}{2}\times AB\times OC$
$=\frac{1}{2}\times 14\times 7$
$=49$ sq cm
Area of shaded portion in semicircle $=77-49=28$ sq cm
Total area of shaded portion $=28+38.5=66.5$ sq cm