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You are designing a 256 cm^3 right circular cylindrical can whose manufacture will take waste into account. There is no waste in cutting the aluminum

You are designing a 256 cm^3 right circular cylindrical can whose manufacture will take waste into account. There is no waste in cutting the aluminum for theside, but the top and bottom of radius r will be cut from squares that measure 4r units on a side. The total amount of aluminum used up by the can will therefore be A=32r^2+2rh,

where h is the height of the right circular cylindrical can. What is the ratio of h to r for the most economicalcan?

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