SOLUTION: A park has just installed a circular fountain in 8 meters diameter. The park wants to pave a 1.5 meter wide path around the fountain. If paving costs 10 dollars per square meter, f

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Question 571232: A park has just installed a circular fountain in 8 meters diameter. The park wants to pave a 1.5 meter wide path around the fountain. If paving costs 10 dollars per square meter, find the cost to the nearest dollar of the paved path around the fountain.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
fountain is 8 meters in diameter.
this makes the radius equal to 4 meters.
add 1.3 meters to make the radius of the outer edge of the path around the fountain equal to 5.3 meters.
the area of the fountain is pi*r^2 = pi*4^2 = 16*pi square meters.
the area of the path plus the fountain is pi*r^2 = pi*5.3^2 = 28.09*pi square meters.
the difference between the larger area and the smaller area is the area of the path around the fountain.
this is equal to 28.09*pi - 16*pi which is equal to 12.09*pi square meters.
if you multiply this by $10.00 a square meter, then you get a total cost of $120.9 * pi dollars.
this results in $379.818 dollars which rounds to $380 dollars.
the diagram shows how this was done.