An arc of length 20π cm subtends an angle of 144°
Question:

An arc of length 20π cm subtends an angle of 144° at the centre of a circle. Find the radius of the circle.

Solution:

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

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

It is given $l=20 \pi \mathrm{cm}$ and angle $\theta=144^{\circ}$.

Now we substitute the value of l and θ in above formula to find the value of radius r of circle.

$20 \pi \mathrm{cm}=\frac{144^{\circ}}{360^{\circ}} \times 2 \pi r$

$r=\frac{20 \pi \times 360^{\circ}}{2 \pi \times 144^{\circ}} \mathrm{cm}$

$r=25 \mathrm{~cm}$