Question

What is the radius of a circle with sector area 12 pi in ^2 and central angle of 3pi/2 radians?

Radius= ___

Answer 1

4

Explanation:

Area of Sector is

`(x)/(2\pi) \pi {r}^(2)`

, where x is the central angle is radians.

If we know the area is 12 pi., central angle js 3 pi/2, we can solve for the area.

`( (3\pi)/(2) )/(2\pi) \pi {r}^(2) = 12\pi`

`(3)/(4) \pi {r}^(2) = 12\pi`

`(3)/(4) {r}^(2) = 12`

`{r}^(2) = 16`

`r = 4`

So the radius is 4