SOLUTION: Find the area of the region that lies outside of the circle x^2+y^2=1 but iside of the circle x^2+y^2-2y=8. Round the decimal answers to two decimal places

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Question 1092598: Find the area of the region that lies outside of the circle x^2+y^2=1 but iside of the circle x^2+y^2-2y=8. Round the decimal answers to two decimal places
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The first circle is centered at (0,0) with a radius of 1.
Complete the square to find the center and radius of the second circle.
x%5E2%2B%28y%5E2-2y%29=8
x%5E2%2B%28y%5E2-2y%2B1%29=8%2B1
x%5E2%2B%28y-1%29%5E2=9
So the second circle is centered at (0,1) with a radius of 3.
So the first circle is completely contained in the second.
Use the circle area formula to get the answer,
A=pi%2AR%5B2%5D%5E2-pi%2AR%5B1%5D%2A2
A=pi%2A%283%29%5E2-pi%2A%281%29%5E2
A=pi%289-1%29
A=8pi