Question 176925: A circular pool is surrounded by a brick walkway 3 m wide. Find the radius of the pool if the area of the walkway is 198 m^2 Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! Draw a picture of the situation -- it'll help you visualize the problem.
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"area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway"
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Let R = radius of pool
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"area of the circle bounded by the outside edge of the walkway" is:
(pi)(R+3)^2
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"area of the pool" is:
(pi)R^2
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Our equation is:
(pi)(R+3)^2 - (pi)R^2 = 198
factoring the left:
(pi)((R+3)^2 - R^2) = 198
expanding:
(pi)(R^2+6R+9 - R^2) = 198
(pi)(6R+9) = 198
6R+9 = 198/(pi)
6R = 198/(pi) - 9
R = (198/(pi) - 9)/6
R = (198/(3.14) - 9)/6
R = (63.057 - 9)/6
R = 54.057/6
R = 9.01 meters
