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Question 679452: How do I solve this?
Q. Given two concentric circles, find the length of the radius of the inner circle.
knowns:
Area of the annulus is 40pi square inches.
The radius of the outer circle is (one inch plus two times the radius of the inner circle).
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! Let r = the radius of the inner circle.
Then the radius of the outer circle is
(1) radius of outer = (1 + 2r)
Using the formula for the area of a circle (pi*radius^2), and taking the difference between the outer circle area and inner circle area gives us
(2) 40pi = pi*((1+2r)^2 - r^2) which reduces to
(3) 40 = 1 + 4r + 4r^2 - r^2 or
(4) 3r^2 + 4r - 39 = 0 which factors into
(5) (3r + 13)*(r - 3) = 0, which gives the roots
(6) r = (-13/3, 3)
Since the radius must be positive we select
(7) r = 3
Let's see if this is correct using (2)
Is (40pi = pi*((1+2*3)^2 - 3^2))?
Is (40pi = pi*(49 - 9))?
Is (40pi = 40pi)? Yes
Answer: The radius of the inner circle is 3 inches.
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