Answer:
[tex]\frac{10}{3}[/tex] units
Step-by-step explanation:
Recall that the area of a sector is [tex]A=\frac{r^2\theta}{2}[/tex] where [tex]r[/tex] is the radius and [tex]\theta[/tex] is the angle of the sector (measured in radians).
Therefore, the radius of the sector is:
[tex]A=\frac{r^2\theta}{2}[/tex]
[tex]\frac{100\pi}{27}=\frac{r^2(\frac{2\pi}{3})}{2}[/tex]
[tex]200\pi=27r^2(\frac{2\pi}{3})[/tex]
[tex]200\pi=r^2(\frac{54\pi}{3})[/tex]
[tex]200\pi=r^2(18\pi)[/tex]
[tex]\frac{200}{18}=r^2[/tex]
[tex]\frac{100}{9}=r^2[/tex]
[tex]\frac{10}{3}=r[/tex]
So, the radius of the sector is [tex]\frac{10}{3}[/tex] units.
