Question

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

Answer 1

We know that

$\theta =\frac{l}{r}\to \left(1\right)$

We are given that

Area of circle is $64\pi sq.cms$

therefore $A=64\pi$

$\pi r^2=64\pi$

$r^2=64$

$r=8cms$

Now we are also given that

the perimeter of sector of a

circle is $l=56cms$

Now, Area of sector is given by

$a=\frac{1}{2}{r}^2\theta =\frac{1}{2}{r}^2\frac{l}{r}$ (From $\left(1\right)$)

$a=\frac{lr}{2}=\frac{56\times 8}{2}=224$

$a=224sq.cms$

$\to$ The are of sector is $224sq.cms$