# The length of an arc of a circle is 12

The length of an arc of a circle is 12 cm. The corresponding sector area is 108 cm${}^{2}$. Find the radius of the circle.
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Erika Ayers
If $\theta$ is the central angle in radians and $r$ is the radius, we can write the two following equations: $r\theta =12$ and $\frac{1}{2}\theta {r}^{2}=108.$ Dividing the first equation into the second, we have that $\frac{1}{2}r=9,$ so r=18.