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. (a) 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.) vcone vcylinder = (b) determine the ratio of the volume of a paraboloid (a parabola rotated about the y axis) to the volume of a cylinder with the same height and base radius: