The heights of a cone, cylinder and hemisphere and equal. If their radii are in the ratio 2:3:1, then the ratio of the their volumes is

heights of a cone = height of cylinder = radius of hemisphere = r units = 1

volume of cone = $$ \frac{1}{3} \pi r1^2 h $$

volume of cylinder = $$ \pi r2^2 h $$

volume of hemisphere = $$ \frac{2}{3} \pi r^3 $$

ratio of the their volumes = $$ \frac{1}{3} \pi r1^2 h : \pi r2^2 h :  \frac{2}{3} \pi r^3 $$ 

                                       = $$ \frac{1}{3} \times \pi \times 4 \times 1 : \pi \times 9 \times 1 : \frac{2}{3} \times \pi \times 1 $$

                                        = $$ \frac{4}{3} : 9 : \frac{2}{3} $$

                                        =  4 : 27 : 2