Question

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

Answer 1

In the given sector,

$\theta ={200}^0,A=770c{m}^2$ $I=?$

$A=\frac{\pi r^2\theta }{{360}^0}$

$\Rightarrow r^2=\frac{A\times {360}^0}{\pi \theta }=\frac{770\times {360}^0\times 7}{22\times {200}^0}\Rightarrow r^2=441\Rightarrow r=21cm$

$r=21cm$

Now, lenght of arc $I=\frac{2\pi r\theta }{{360}^0}$

$=2\times \frac{22}{7}\times \frac{21\times {200}^0}{{360}^0}=\frac{220}{3}cm=73\frac{1}{3}cm$

Hence, the required lenght of arc $=73\frac{1}{3}$ cm