Question

In a circle of radius $6$ cm, a chord makes an angle of $110$ ${}^{\circ }$ at the centre of the circle. Find the area of the sector OAB.

Answer 1

$\Rightarrow$ Radius of a circle $\left(r\right)=6cm$

$\Rightarrow$ $\theta ={110}^o$

$\Rightarrow$ Area of the sector $=\frac{\theta }{{360}^o}\left(\pi r^2\right)$

Where, $\theta$ is angle subtended at a center.

$\pi r^2$ is area of a circle.

$\Rightarrow$ Area of the sector $=\frac{{110}^o}{{360}^o}\times \frac{22}{7}\times (6{)}^2$

$\therefore$ Area of the sector $OAB=\frac{11\times 22\times 36}{36\times 7}=34.57c{m}^2$