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

Arc length$=20\pi cm\Rightarrow \frac{\theta }{360°}\times 2\pi r=20\pi$

$\Rightarrow \frac{144°}{360°}\times r=10\Rightarrow r=\frac{360\times 10}{144}=25cm$