Question

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

Answer 1

Step 1: Given data
Length of arc $l=37.4$ cm
Angle $\left(\theta \right)={60}^{\circ }=60\times \frac{\pi }{180}=\frac{\pi }{3}$ radian
Step 2: Solve for radius of circle $r$
We know that $r=\frac{l}{\theta }$, where $\theta$ is in radian
$\Rightarrow r=\frac{37.4}{\frac{\pi }{3}}\Rightarrow r=37.4\times \frac{7\times 3}{22}$
$\Rightarrow r=35.7$ cm