Given: An sector with a central angle-
[tex]\theta=\frac{2\pi}{3}[/tex]And area,
[tex]Area=\frac{100\pi}{27}\text{ sq units}[/tex]Required: To determine the radius of the sector.
Explanation: The area of the sector when the central angle is in radians is given by the formula-
[tex]Area=\frac{1}{2}r^2\theta\text{ sq units}[/tex]Substituting the values into the formula as-
[tex]\frac{100\pi}{27}=\frac{1}{2}(\frac{2\pi}{3})r^2[/tex]Further solving for 'r' as follows-
[tex]\begin{gathered} r=\sqrt{\frac{100}{9}} \\ r=\frac{10}{3}\text{ units} \end{gathered}[/tex]Final Answer: The radius of the sector is-
[tex]r=\frac{10}{3}\text{ units}[/tex]