Archimedes (ca. 287-212 B. C.) was able to use clever geometric means to determine the relative volumes of a cylinder and the cone and paraboloid that would fit snugly into it (1800 years before Newton and Leibniz). With calculus, you don't have to be a genius to reach the same conclusions.

Determine the ratio of the volume of a (right circular) cone to the volume of a cylinder with the same height and base radius: (First you will need to determine the equation of the line which rotates to generate the cone.)