Length of an arc from the central angle

Text

In a circle of radius $r=15$ cm a central angle of $72^\circ$ subtends an arc $AB$. Find the length of the arc.

Solution

Convert the angle to radians: $72^\circ=\dfrac{72\pi}{180}=\dfrac{2\pi}{5}$. The length of an arc is $L=r\,\theta$ (with $\theta$ in radians): $L=15\cdot\frac{2\pi}{5}=6\pi\approx18.85\ \text{cm}.$ $\boxed{L=6\pi\approx18.85\ \text{cm}}$