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(\pi)/(180\degree)=(\pi)/(3)`

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

`18\pi=r\cdot((\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.