Given a right circular cone with the line of symmetry along , and the base along , how can I find the maximum volume paraboloid (parabola revolved around the y-axis) inscribed within the cone? Maximising the volume of the paraboloid relative to the volume of the right circular cone. In 2-D, the parabola has 2 points of tangency to the triangle, one of each side of the line of symmetry. I have tried using the disk method to find the volume of the cone, and the parabola, both with arbitrary equations such as , and , but I end up with a massive equation for several variables, instead of a simple percentage answer. Any help is appreciated! Thanks in advance.