SOLUTION: A sector of a circle has an angle at the centre of pi/4 and a perimeter of 12. Work out the radius of the circle.

Algebra ->  Trigonometry-basics -> SOLUTION: A sector of a circle has an angle at the centre of pi/4 and a perimeter of 12. Work out the radius of the circle.      Log On


   

Question 854810: A sector of a circle has an angle at the centre of pi/4 and a perimeter of 12. Work out the radius of the circle.
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
r is the unknown radius.
The circumference (of the circle) would be 2*pi*r, and the arc length portion of the sector is %28%28pi%2F4%29%2F%282%2Api%29%29%2A%282%2Api%2Ar%29; which we should simplify NOW:

ArcPortion=%28pi%2Ar%29%2F4

The perimeter of the sector is the sum of two of r and the ArcPortion:
Given that the perimeter is 12,
highlight%282r%2B%28pi%2Ar%29%2F4=12%29
This is now a fairly simple equation easily solvable for r.