Answer:
[tex]r=5[/tex]
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:
[tex]\begin{gathered} S=r\theta\Rightarrow(1) \\ r=? \\ S=\frac{10\pi}{3} \\ \theta=\frac{2\pi}{3} \end{gathered}[/tex]
Plugging in the known information in equation (1) and solving for the unknown variable r gives the following answer:
[tex]\begin{gathered} \begin{equation*} S=r\theta \end{equation*} \\ \frac{10\pi}{3}=r\frac{2\pi}{3}\rightarrow10=r2 \\ r=\frac{10}{2}=5 \\ r=5 \end{gathered}[/tex]
Therefore the value of the radius is 5:
