Question

The area of a sector of a circle of radius $2cm$ is $\pi {cm}^2$. Find the angle contained by the sector.

Answer 1

Given that, Area of a sector $=\pi {cm}^2$

$r=2cm$

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

Where, $\theta$ is the angle contained by sector and

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

$\therefore$ $\pi =\frac{\theta }{{360}^o}\times \pi \times (2{)}^2$

Solving for $\theta$:

$\therefore$ $\theta =\frac{{360}^o}{4}={90}^o$