The area of the entire circle is of course [tex]\pi r^2[/tex]
The area of the sector is the fraction of the circle's area,
[tex]\dfrac{110}{360} \ \pi r^2[/tex]
We're told that area is 50.
[tex]\dfrac{110}{360} \ \pi r^2 = 50[/tex]
[tex]r^2 = \dfrac{50 \cdot 360}{110 \pi} = \dfrac{1800}{11 \pi}[/tex]
[tex]r = \sqrt{ \dfrac{1800}{11 \pi}} = 30 \sqrt{ \dfrac{2}{11 \pi} }[/tex]
