Question

Area fo a sector of central angle ${200}^{\circ }$ of a circle is $770c{m}^2$. Find the length of the corresponding arc of this sector.

Answer 1

Given that the central angle of the sector is ${200}^{\circ }$.

$\to$ $\theta$= ${200}^{\circ }$.

And, Area of the sector = 770 ${cm}^2$

Area of the sector = $\pi r^2{\theta }^{\circ }\frac{1}{{360}^{\circ }}$

$\to$ 770 = $\frac{22}{7}{r}^2\frac{{200}^{\circ }}{{360}^{\circ }}$

$\to$$r^2$= $\frac{1940400}{4400}$

$\to$$r^2$= 441

$\to$ r = $\sqrt{441}$ \

$\to$ r = 21 cm

We now calculate the length of the corresponding arc of this sector

$\to$ 200. 21.$\frac{\pi }{{180}^{\circ }}$

$\to$ 200.21.$\frac{22}{7}$.$\frac{1}{180}$

= $\frac{9240}{126}$

= $\frac{220}{3}$

= 73 $\frac{1}{3}$ cm - Answer.