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

Answer:

4

Step-by-step explanation:

Area of Sector is

$\frac{x}{2\pi} \pi {r}^{2}$

, 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.

$\frac{ \frac{3\pi}{2} }{2\pi} \pi {r}^{2} = 12\pi$

$\frac{3}{4} \pi {r}^{2} = 12\pi$

$\frac{3}{4} {r}^{2} = 12$

${r}^{2} = 16$

$r = 4$

So the radius is 4