Question

Area of a sector of a circle of radius $15cm$ is $30c{m}^2$. Find the length of the arc of the sector.

Answer 1

Area of sector of circle $=30c{m}^2$

radius of circle $=15cm$

Area of sector $=\frac{\theta }{360}\times \pi r^2$

$\frac{\theta }{360}=\frac{A}{\pi r^2}=\frac{30}{\pi \times 15\times 15}=\frac{2}{15\pi }$

now length of arc $=2\pi r=\frac{\theta }{360}=2\pi \times 15\times \frac{2}{15}$

Length of arc $=4cm$