Question

The area of a sector of a circle with a central angle of 15π rad is 18 m².

Find the radius of the circle.

I set up my equation as:

18m^2=(1/2)(r^2)(1/5 pi)

i isolate r^2 by dividing both sides by (1/2) and (1/5 pi, getting:

180pim^2=r^2

i then take the square root of each and get 13.4164 pi=r

this is a problem, because i am using WAMAP and it does not allow decimal approximations and it wants pi left in the answer. did i go wrong somewhere? thanks

Answer 1

well, if you have pi/10 r^2 = 18, you wind up with

r^2 = 180/pi
r = 3√(20/pi)

Now, if your angle is 1/(5pi), then you are correct to have r^2 = 180pi

But, √(180pi) is not √180 * pi. When you take the root, you also have to include pi inside: √(180pi) = 3√(20pi).