Question

The perimeter of a sector of a circle, of area $25\pi sqcms$, is $20cms$. Find the area of sector.

Answer 1

Area of a circle=$25\pi c{m}^2$

$\pi r^2=25c{m}^2$

$r=5cm$

Perimeter of sector$2r+\frac{Q}{360}\times 2\pi r$

$\Rightarrow 20=2\times 5+\frac{Q}{360}\times 2\pi \times 5$

$\Rightarrow \frac{Q}{360}\times 10\pi =10$

$\Rightarrow \frac{Q}{360}=\frac{1}{\pi }$

Now, Area of sector =$\frac{Q}{360}\times \pi r^2$

$=\frac{1}{\pi }\times \pi \times 5\times 5$

$=25c{m}^2$