Question

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

Answer 1

Area of the sector $=\frac{1}{2}{r}^2\theta$

$r=36cm$

$54\pi =\frac{1}{2}\times 36\times 36\times \theta$

$\frac{54\times \pi }{18\times 36}=\theta$

$\therefore \theta =\frac{\pi }{12}=\frac{180}{12}={15}^{\circ }$

Length of arc = Radius $\times$ angle

$S=r\theta$

$S=36\times 15$

$S=540cm$