Ratio of heights of cylinder and hemisphere

Let radius of both parts be $r$, and height of cylindrical part be $h$. Volume of cylindrical part $= \pi r^2 h$ Volume of hemispherical part $= \frac{2}{3}\pi r^3$ Given $\pi r^2 h = \frac{2}{3}\pi r^3 \implies h = \frac{2}{3}r$. Height of hemispherical part is its radius $r$. Ratio $= \frac{h}{r} = \frac{\frac{2}{3}r}{r} = \frac{2}{3} = 2 : 3$.