Q.Find the radius of the circle in which central angle of $60°$ intercepts an arc of length 37.4 cm.

For a sector of a circle of radius $r$ whose central angle is $\theta$ radians, the length $S$ of the enclosed arc is directly proportional to $\theta$ (as a fraction of the full circumference $2\pi r$ corresponding to the full angle $2\pi$):

$\frac{S}{2\pi r} = \frac{\theta}{2\pi} \quad\Longrightarrow\quad S = r\theta$ …