Question

Find the radius of the circle in which a central angle of ${60}^{\circ }$ intercepts an arc of length $37.4cm.$ (use $\pi =\frac{22}{7}$)

Answer 1

Step 1 :
Given data
Length of $arcl=37.4cm$
Angle $\left(\theta \right)={60}^{\circ }=60\times \frac{\pi }{180}=\frac{\pi }{3}$ radian

Step 2 :
We know that $r=\frac{l}{\theta }$, where $\theta$ is in radians.
$\Rightarrow r=\frac{37.4}{\left(\frac{\pi }{3}\right)}$
$\Rightarrow r=37.4\times \frac{7\times 3}{22}$
$\Rightarrow r=35.7cm$.