Question

The perimeter of a sector of a circle of area $64\pi sqcms$ is $56cms$. Find the area of sector.

Answer 1

A] area$=64\pi$

$\pi r^2=64\pi$

$r^2=64$

$r=8cm$

Perimeter of sector = 2r (length of area)

$56=2\times 8\times l$

$\frac{56}{16}=l$

$\therefore l=\frac{7}{2}$

So, area of sector $=\frac{1}{2}\times l\times r$

$\frac{1}{2}\times \frac{7}{2}\times 8=14c{m}^2$