A circle with area 9π has a sector with a central angle of 17π/9 radians. What is the area of the sector?

8.5pi

Step-by-step explanation:

We can solve this problem with a rule of three.

The area of the whole circle is represented by a sector with central angle of 2*pi. So, if we want to find the area of a sector that has a central angle of 17pi/9, we can use the following logic:

sector of 2pi - > area equal to 9pi

sector of 17pi/9 - > area equal to X

2pi / (17pi/9) = 9pi / X

18 / 17 = 9pi / X

X = 17 * 9pi / 18 = 17pi / 2 = 8.5pi