Question

In a circle of radius $21cm$ , an arc subtends an angle of ${60}^o$ at the centre.Find
(i) The length of the arc
(ii) Area of sector.

Answer 1

Given:-

Angle subtended by the arc $\left(\theta \right)=60°$

Radius of circle $\left(r\right)=21cm$

• (i) Length of arc $\left(l\right)=\frac{\theta }{360°}\times 2\pi r$
  

$\Rightarrow l=\frac{60°}{360°}\times (2\times \frac{22}{7}\times 21)=\frac{1}{6}\times (6\times 22)=22cm$

• (ii) Area of sectore formed by the arc $\left(A\right)=\frac{\theta }{360°}\times \pi r^2$

$\Rightarrow A=\frac{60°}{360°}\times (\frac{22}{7}\times {\left(21\right)}^2)=\frac{1}{6}\times 11\times 6\times 21=231{cm}^2$