Question

What is the value of x in the diagram? A circular pool with a diameter of 18 ft will have a uniform 4 ft concrete walkway poured around it. If the concrete cost $4.25 a square foot, how much will it cost for the concrete?

Answer 1

If you visualize the problem, there are two concentric circles, the pool, and the pool plus the walkway. So, we have to subtract the area of these two concentric circles to find the walkway.

Bigger circle: Pool plus walkway
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diameter = 18 + 4(2)   -- this is because there is 2 ft of walkway at each far end
diameter = 26 ft
Area = pi*(26/2)^2
Area = 530.93 ft2

Smaller circle:pool
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diameter = 18 ft
Area = pi*(8/2)^2
Area = 50.27 ft2

Area of walkway
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A = 530.93 - 50.27
A = 480.66 ft2

Then the cost would be
Cost = $4.25 * 480.66
Cost = $2,042.81