Question 135729: A circular pond 26 yd in diameter is surrounded by a gravel path 2 yd wide. The path is to be replaced by a brick walk costing $50 per square yard. How much will the walk cost?
Answer by AlexxsDad(4)   (Show Source):
You can put this solution on YOUR website! The gist of this problem is realizing that, in order to get the area of the walkway, we subtract the area of a smaller circle from that of a larger one. The larger circle has a diameter of 28 yd (2 yd larger than the 26 yd circle), minus the 26 yd circle.
So a 28 yd circle has a radius of 14 yd, and an area of 2 * pi * 14^2
The area of the 26 yd circle is 2* pi * 13^2.
(Radius is half of diameter).
So, the area of the large circle is 2 * pi * 196 = 1231 sq yd (approx)
and the area of the smaller is 2 * pi * 169 = 1062 sq yd (approx)
(Always thought there was a beauty to these two adjacent squares 169 and 196!)
So the area of the walk would be 1231 sqyd - 1062 sqyd = 169 sqyd
This has to be multiplied by $50/sqyd to find the cost:
169 sqyd * $50/sqyd = $8450
(For your future study of "dimensional analysis," can you see how even the "sqyd" cancels out?)
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