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?
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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) (Show Source): You can put this solution on YOUR website!
Answer by TutorDelphia(193) (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
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
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.
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