Question

Area of sector of circle of radius 36 cm is 54$\pi c{m}^2$ . Find the length of the corresponding arc of the sector.

Answer 1

Given area of sector of circle $=54\pi$ $c{m}^2$

Radius of circle$=36$cm

Now area of circle$=\pi r^2\times \left(\frac{\theta }{360}\right)$

$54\pi =\frac{\theta }{360}\times \pi r^2$

$\frac{\theta }{360}=\frac{54}{36\times 36}$ …………$\left(1\right)$

and length of arc$=2\pi r\left(\frac{\theta }{360}\right)$

$L=2\pi \times 36\times \frac{54}{36\times 36}$

[Length of arc $=3\pi cm$].