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## Homework Statement

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?

## Homework Equations

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

The surface area would be pi(r)^2+pi(R+r)sqrt((r-R)^2+h^2

## The Attempt at a Solution

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.