A cone, a hemisphere and a cylinder stand on equal bases and have the same height. What is the ratio of their volumes, in that order?

A hemisphere's height equals its own radius, so the common height is $h=r$. Then the cone is (1/3)π$r^{2}h=(1/3)$π$r^3$, the hemisphere is (2/3)π$r^3$ and the cylinder is π$r^2$$h$ = π$r^3$. Dividing all three by (1/3)π$r^3$ gives 1 : 2 : 3. The trap 1 : 3 : 2 swaps the last two, forgetting that a hemisphere must hold less than the cylinder enclosing it; 1 : 1 : 1 confuses equal bases and heights with equal volumes.