Question

Find the radius of the circle in the figure to the right.

Answer 1

The length of an arc, the radius of a circle and the central angle that contains that arc are related as follows:

`s=r\theta`

From the figure, we have that:

`\begin{gathered} s=17\pi \\ \theta=(4\pi)/(3) \end{gathered}`

Substitute those values into the equation to find the value of r:

`\begin{gathered} 17\pi=r*(4\pi)/(3) \\ \Rightarrow17\pi*(1)/(\pi)=r*(4\pi)/(3)*(1)/(\pi) \\ \Rightarrow17=r*(4)/(3) \\ \Rightarrow17*(3)/(4)=r*(3)/(4)*(4)/(3) \\ \Rightarrow r=17*(3)/(4) \\ \Rightarrow r=(17*3)/(4) \\ \therefore r=(51)/(4) \end{gathered}`

Therefore, the radius of the circle is:

`(51)/(4)`