SOLUTION: QR is an arc of a circle with a center P. If the length of the arc is 6pi and the degree of the angle formed at center P is 30 degrees, what is the area of the sector PQR? The an

Algebra ->  Algebra  -> College  -> Linear Algebra -> SOLUTION: QR is an arc of a circle with a center P. If the length of the arc is 6pi and the degree of the angle formed at center P is 30 degrees, what is the area of the sector PQR? The an      Log On


   

Question 467255: QR is an arc of a circle with a center P. If the length of the arc is 6pi and the degree of the angle formed at center P is 30 degrees, what is the area of the sector PQR?
The answer is 108pi.
Please help me understand how they got this answer.
Thank you!

Found 2 solutions by Big Poop, TutorDelphia:
Answer by Big Poop(157) About Me  (Show Source):
Answer by TutorDelphia(193) About Me  (Show Source):
You can put this solution on YOUR website!
30 degrees is 30/360 which reduces to 1/12 of the whole circle (there are 360 degrees in a circle).
if 6pi is 1/12 of the circumference than the whole circumference can be found from 6pi*12 which gives us 72pi as my circumference.
Using the formula c=2pi%2Ar
72pi=2%2Api%2Ar
36=r
I now know that my radius of the circle is 36.
Therefore my area of the circle is 1296 pi from the formula A=pi%2Ar%5E2
Now that we have the area of the whole circle, I can just divide it by 12 to get the area of the sector. So my area is 108 pi as you said.