Question

Area of a sector of central angle ${200}^0$ of a circle is 770 $c{m}^2$. The length of the corresponding arc of this sector is

• A. $73\frac{1}{3}cm$
• B. $156\frac{1}{3}cm$
• C. $7\frac{1}{3}cm$
• D. $22\frac{1}{3}cm$

Answer 1

The correct option is A $73\frac{1}{3}cm$

$Given-OAPBisasectorwithcentralangle=\angle AOB=\theta ={200}^{o}andar.sector=770{cm}^2.Tofindout-ThelengthofthearcAPB=l=?Solution-Lettheradiusofthesectorber.Thenar.sector=\frac{\theta }{{360}^o}\times \pi \times r^2=\frac{{200}^o}{{360}^o}\times \frac{22}{7}\times r^2=770⟹r=\sqrt{770\times \frac{{360}^o}{{200}^o}\times \frac{7}{22}}cm=21cm.\therefore ThelengthofthearcAPB=l=\frac{\theta }{{360}^o}\times 2\times \pi \times r=\frac{{200}^o}{{360}^o}\times 2\times \frac{22}{7}\times 21cm=\frac{220}{3}cm=73\frac{1}{3}cmAns-OptionA.$