# How do you find the radius with the area of a sector of a circle with a sector which its area is 12pi cm^2 and the angle is 120°?

Dec 3, 2017

#### Explanation:

A full circle has 360°, so 120° is 1/3 of the circle. We can use this to find the full area of the circle from which the sector was cut:

(120°)/(360°)=(12pi)/x \rightarrowx=36pi

Since the full area of the circle is $36 \pi$ and the area of a circle is $A = \pi \cdot {r}^{2}$, we know that:

$\pi \cdot {r}^{2} = 36 \pi$
${r}^{2} = 36$
$r = 6$
We ignore the negative value since the radius should be positive.

Since the units of the area are cm^2, the units for the radius are just cm.