- Consider right circular cone-shaped paper cups available when getting a drink from a water cooler. To save resources one seeks to maximize the volume of liquid a cup holds when each has the same surface area so the same amount of paper is used for each cup. What is the optimal relationship between the base radius r and the height h of the optimal cone?
I'm confused on how to even approach this. We are currently doing Kuhn-Tucker conditions and Lagrange multiplier rules.