The ratio of volume of a cylinder : volume of cone : volume of hemisphere of same radius and same height is

Using the volume formulas for a cylinder ($\pi r^2 h$), a cone ($\frac{1}{3}\pi r^2 h$), and a hemisphere ($\frac{2}{3}\pi r^3$), substitute $h = r$ to maintain the same height. This gives volumes of $\pi r^3$, $\frac{1}{3}\pi r^3$, and $\frac{2}{3}\pi r^3$ respectively. The ratio of these volumes is $1 : 1/3 : 2/3$, which simplifies to $3 : 1 : 2$.

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