Question 571232
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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.



Solved correctly.