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°?

1 Answer
Dec 3, 2017

The radius is 6 cm.


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 #36pi# and the area of a circle is #A=pi*r^2#, we know that:

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.