Question

The adjacent figure shows two arcs $P$ and $Q.$ Arc $P$ is part of the circle with centre $O$ and radius $OA=10cm$. Arc $Q$ is a part of the circle with centre $M$ and radius $AM=5cm,$ where $M$ is the mid-point of $AB.$ Area enclosed by the arc $Q$ and chord $AB$ is

• A. $25\pi c{m}^2$
• B. $\frac{25}{2}\pi c{m}^2$
• C. $20\pi c{m}^2$
• D. $\frac{20}{2}\pi c{m}^2$

Answer 1

The correct option is B

$\frac{25}{2}\pi c{m}^2$

Area enclosed by the arc $Q$ and chord $AB$ is the semi-circle, $AQB$
So, area of semi-circle $AQB=\frac{1}{2}\times \pi r^2=\frac{1}{2}\times \pi \times 5\times 5=\frac{25}{2}\pi c{m}^2$