Given the ratio of heights: \( \frac{h_1}{h_2} = \frac{2}{3} \),

\( h_2 = \frac{2h_1}{3} \)

The ratio of radii: \( \frac{r_1}{r_2} = \frac{9}{8} \),

\( r_2 = \frac{9r_1}{8} \)

The volume of the first cylinder:

\( v_1 = \pi \left(\frac{9r_1}{8}\right)^2 \left(\frac{2h_1}{3}\right) \)

\( = \pi r_1^2 2h_1 \left(\frac{27}{32}\right) \)

The volume ratio:

\( v = \frac{\pi r_1^2 2h_1 \times \frac{27}{32}}{\pi r_1^2 2h_1} = \frac{27}{32} \)

The volume ratio of the second cylinder to the first:

\( v_2 : v_1 = 27 : 32 \)