Filling Revolutionary Vessels

This applet allows you to make "vases" that are volumes of revolution of a curve around an axis of symmetry. Having made such a vessel you can fill it with a 'liquid' and explore how the volume of the liquid in the vessel varies with the height of the liquid in the vessel. CHALLENGE - given the shape of the function dV(h)/dh can you infer the shape of the "vase"? if yes, how? If no, why not? Would you pose this question to your students? What questions would you pose for students?