Question

find the radius of a circle containing 60° arc of a circle whose length is 18π meters

Answer 1

Our situation is this:

First, we need to convert our angle, which is written in degrees, to radians.

$60\degree\cdot\frac{\pi}{180\degree}=\frac{\pi}{3}$

Now, we have the equation (for the length of an arc in a circle):

$18\pi=r\cdot(\frac{\pi}{3})$

Let us solve it:

$3\cdot18\cdot\pi=r\cdot\pi$$3\cdot18=r$$r=54$

Thus, the radius of our circle is 54 units.