Q.Find the length of an arc of a circle which subtends an angle of $108°$ at the centre, if the radius of the circle is 15 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 $2\pi$):

A degree measure must first be converted to radian ($\theta^{c}=\theta°\times\frac{\pi}{180}$) before this formula can be used. The same formula models any physical situation shaped like an arc swept at a fixed radius -- a pendulum bob tracing its swing, an animal on a tether walking a circular path, or a point on a rotating wheel or clock hand -- with the "radius" being the pendulum length, rope length or hand length as appropriate.