Question

Area of sector of central angle 200⁰ of a circle is 770 cm² . Find the length of the corresponding arc of this sector .

Answer 1

Area of the sector = 770 cm²
Central angle, $\theta ={200}^{°}$
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{sector}=\frac{\theta }{360}\times \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{circle} \\ \Rightarrow 770=\frac{200}{360}\times \mathrm{\pi }{r}^2 \\ \Rightarrow r\approx 21 \end{gathered}$$
Now, $\mathrm{Area}\mathrm{of}\mathrm{sector}=\frac{1}{2}lr$
$$\begin{gathered} \Rightarrow 770=\frac{1}{2}l\times 21 \\ \Rightarrow l=\frac{220}{3}\mathrm{cm} \end{gathered}$$