Question

Im unsure of how to set up this question so I can do the math to solve it, can you help me?

Answer 1

`r=5`

Step-by-step explanation: We have to find the radius of the circle provided the central angle and the arc-length, the formula used to determine the radius is as follows:

`\begin{gathered} S=r\theta\Rightarrow(1) \\ r=? \\ S=(10\pi)/(3) \\ \theta=(2\pi)/(3) \end{gathered}`

Plugging in the known information in equation (1) and solving for the unknown variable r gives the following answer:

`\begin{gathered} \begin{equation*} S=r\theta \end{equation*} \\ (10\pi)/(3)=r(2\pi)/(3)\rightarrow10=r2 \\ r=(10)/(2)=5 \\ r=5 \end{gathered}`

Therefore the value of the radius is 5: