SOLUTION: You have a sector PQR where QR is the arc of the circle with center P. If the lenght of the arc QR is 6pi, and the angle formed at point P is 30 degrees, what is the area of the se

Algebra ->  Algebra  -> Surface-area -> SOLUTION: You have a sector PQR where QR is the arc of the circle with center P. If the lenght of the arc QR is 6pi, and the angle formed at point P is 30 degrees, what is the area of the se      Log On

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Question 467135: You have a sector PQR where QR is the arc of the circle with center P. If the lenght of the arc QR is 6pi, and the angle formed at point P is 30 degrees, what is the area of the sector PQR?
The answer is 108pi.
I do not understand how they got this answer.
Can you help?
Answer by jim_thompson5910(28549) About Me  (Show Source):
You can put this solution on YOUR website!
Note: 30 degrees = 30%2A%28pi%2F180%29=pi%2F6 radians

Arc length: L=theta%2Ar where theta is the central angle (that subtends, ie cuts, the arc....this angle is in radians) and r is is the radius


So we're given that L=6pi and theta=pi%2F6. So


L=theta%2Ar


6pi=%28pi%2F6%29%2Ar


r=36


which means that the radius of this circle is 36 units.


Area of sector: A=%281%2F2%29r%5E2%2Atheta


A=%281%2F2%29r%5E2%2Atheta


A=%281%2F2%29%2836%29%5E2%2A%28pi%2F6%29 plug in r=36 and theta=pi%2F6


A=%281%2F2%29%281296%29%2A%28pi%2F6%29


A=%281296pi%29%2F%2812%29


A=108pi


So the area is 108pi