1. ## Urgent need of help with finding radius

A central angle of 60degrees subtends an arc of 18pi inches. Find the radius of the circle.

do you use this: S=2*pi*r?

If so, how do you use it? I know that when r = 1, the central angle = the arc. However, you need to find the radius in this problem. So what do I do?

2. Originally Posted by lax600
A central angle of 60degrees subtends an arc of 18pi inches. Find the radius of the circle.

do you use this: S=2*pi*r?

If so, how do you use it? I know that when r = 1, the central angle = the arc. However, you need to find the radius in this problem. So what do I do?
Change your angle into radians (it's the simplest way) bearing in mind that $\displaystyle 180^o = \pi \text{rad}$

Then use $\displaystyle r = \frac{l}{\theta}$

Spoiler:
$\displaystyle r = \frac{18\pi}{\frac{\pi}{3}} = 18\pi \times \frac{3}{\pi} = 54 \text{inches}$

3. Originally Posted by lax600
A central angle of 60degrees subtends an arc of 18pi inches. Find the radius of the circle.

do you use this: S=2*pi*r?

If so, how do you use it? I know that when r = 1, the central angle = the arc. However, you need to find the radius in this problem. So what do I do?
$\displaystyle s = r\theta$ , where $\displaystyle \theta$ is the central angle in radians

4. "A central angle of 60degrees subtends an arc of 18pi inches. Find the radius of the circle. do you use this: S=2*pi*r? If so, how do you use it? I know that when r = 1, the central angle = the arc. However, you need to find the radius in this problem. So what do I do?"

theta = 60 degrees = pi/3

S = 18 pi

if S = r(theta)

r = S/theta = (18 pi)/(pi/3) =18(3) =