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Calculus and Beyond Homework Help
Minimization of a paper cup
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[QUOTE="tjc9, post: 5969041, member: 643434"] [h2]Homework Statement [/h2] company manufactures paper cups that are designed to hold 8 fluid ounces each. The cups are in the shape of a frustum of a right circular cone (so the top and bottom of the cup are circles, not necessarily of the same size, and the side profile is that of a trapezoid). What are the dimensions for a paper cup that minimizes the amount of material used?[h2]Homework Equations[/h2] [LEFT][SIZE=4][COLOR=rgb(5, 5, 5)]The volume of the cup would be pi/3(R^2+Rr+r^2)h The surface area would be pi(r)^2+pi(R+r)sqrt((r-R)^2+h^2[/COLOR][/SIZE][/LEFT] [h2]The Attempt at a Solution[/h2] Know that I'd need to hold volume constant at V=8 fl. oz. or 14.4375 in.^3. Know I need to minimize the surface area of the cup. I solved for h in the volume equation then substituted that into the area equation. I don't know where to go from there because if you take the partial derivatives it becomes way too complicated. [/QUOTE]
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Minimization of a paper cup
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