Question

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°?

Answer 1

The radius is 6 cm.

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

`pi*r^2=36pi`
`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.