SOLUTION: Maximum area of the rectangular section of a 300 meter running track with semicircles on the ends. Both exact and approximate values

Question 901319: Maximum area of the rectangular section of a 300 meter running track with semicircles on the ends. Both exact and approximate values
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Length = 2pi*r + 2W = 300
r = (150 - W)/2pi
----
Area of rectangle = 2*r*W = W(150-W)/pi
= (150W - W^2)/pi
dA/dW = (150 - 2W)/pi
(150 - 2W)/pi = 0
W = 75 meters
r = 75/2pi --> diameter = 75/pi
Area = 75*75/pi
Area =~ 1790.49 sq m

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