Question

An arc of length $20\pi cm$ subtends an angle of ${144}^{\circ }$ at the centre of a circle. Find the radius of the circle.

Answer 1

We know that the arc length $l$ of a sector of an angle $\theta$ in a circle of radius $r$ is

$l=\frac{\theta }{{360}^o}\times 2\pi r$

$\Rightarrow 20\pi =\frac{144}{360}\times 2\pi r$

$\therefore r=25cm$

Hence, the radius is 25 cm.