Let the heights of the two right circular cylinders be \(h\) units and \(2h\) units, and their radii be \(r_1\) units and \(r_2\) units respectively. \[ \therefore \text{Ratio of circumferences} = 2\pi r_1 : 2\pi r_2 = 3:4 \] So, \[ \cfrac{r_1}{r_2} = \cfrac{3}{4} \] Now, the ratio of their volumes is: \[ = \cfrac{\pi r_1^2 \cdot h}{\pi r_2^2 \cdot 2h} = \left(\cfrac{r_1}{r_2}\right)^2 \cdot \cfrac{1}{2} = \left(\cfrac{3}{4}\right)^2 \cdot \cfrac{1}{2} = \cfrac{9}{16 \times 2} = \cfrac{9}{32} \] \[ \therefore \text{The ratio of their volumes is } 9 : 32 \]