A cone and a cylinder stand on bases of equal radius and hold equal volumes. Find the ratio of the height of the cone to the height of the cylinder.

(1/3)π$r^2$$H$ = π$r^2$$h$ gives $H=3h$, so $H:h=3$ : 1 — the cone has to be three times as tall to hold as much. (1 : 3 reverses it, and comes from remembering only that a cone is a third of a cylinder without asking which quantity is a third.)