Question

The area of the sector formed by the 110 degrees central angle is 50 units^2. What is the radius of the circle?

Answer 1

The area of the entire circle is of course
`\pi r^2`

The area of the sector is the fraction of the circle's area,


`(110)/(360) \ \pi r^2`

We're told that area is 50.


`(110)/(360) \ \pi r^2 = 50`


`r^2 = (50 \cdot 360)/(110 \pi) = (1800)/(11 \pi)`


`r = \sqrt{ (1800)/(11 \pi)} = 30 \sqrt{ (2)/(11 \pi) }`