You are designing a new cylindrical can to hold 1 liter (1000 cubic centimeters) of Jake's Special Paint. Find the dimensions that will minimize the cost of metal to manufacture the can.
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..........[1] ..........[2] Solve [1] for, say, h and sub into [2]: This is what is to be minimized. Differentiate, set to 0 and solve for r. Then h will follow. I believe you will find that the minimum is achieved when the diameter equals the height.
is the derivative: 4 * pi * r - 2000 * r ^ -2
or simplified... 4*pi*r-(2000/x^2)
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