Paper cups - Colegiul National C. Negruzzi (Iași - Roumanie)

Our task to complete is about a waiting clinic in which patients can have water using disposable paper cups in the shape of a cylinder, a cone or a cone frustum. We have to discover a method so we can use as less material as possible, which means a spare of material resources and a minimal cost of production. We realized that we can solve the problem using inequalities and studying functions through derivatives. Thus, we discover minimal area of the cups in terms of a constant volume.