Radius from central angle and arc length

Text

A central angle of $40^\circ$ subtends an arc of length $14$ cm. Find the radius of the circle.

Solution

Convert the angle: $40^\circ=\dfrac{2\pi}{9}$ rad. From $L=r\theta$: $r=\frac{L}{\theta}=\frac{14}{\tfrac{2\pi}{9}}=\frac{14\cdot9}{2\pi}=\frac{63}{\pi}\approx20.05\ \text{cm}.$ $\boxed{r=\dfrac{63}{\pi}\approx20.05\ \text{cm}}$