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. Found 2 solutions by Theo, ikleyn: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.
You can put this solution on YOUR website! .
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.
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Calculations in the post by @Theo are incorrect.
I came to bring a correct solution.
fountain is 8 meters in diameter.
this makes the radius equal to 4 meters.
add 1.5 meters to make the radius of the outer edge of the path around the fountain equal to 5.5 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*5.5^2 = 30.25*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 30.25*pi - 16*pi which is equal to 14.25*pi square meters.
if you multiply this by $10.00 a square meter, then you get a total cost of $142.5 * pi dollars.
this results in $447.6766 dollars which rounds to $447.68 dollars.
After rounding to the closest dollar, you get the answer of 448 dollars.
