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# cup maximum volume

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what is the maximum possible volume of a open top cup that only as 12ft^2 of material. what dimensions (radius, height) will give you the max volume

Apr 5, 2021

Surface area is $2\pi r(h+r)=12\implies rh+r^2=\frac{6}{\pi}$.
We want to maximize $\pi r^2 h$.