Explanation:

- We know that the volume of a cone is given by: \( V = \frac{1}{3} \pi r^2 h \).

- Let the radii of the cones be \( r_1 \) and \( r_2 \), and the heights be \( h_1 \) and \( h_2 \).

- The given ratio of volumes is 11:16, so \(\frac{V_1}{V_2} = \frac{11}{16}\).

- The volume ratio using radii and heights can be expressed as: \(\frac{r_1^2 h_1}{r_2^2 h_2} = \frac{11}{16}\).

- Given the ratio of radii is 3:4, \(\frac{r_1}{r_2} = \frac{3}{4}\).

- Plug the ratio of radii into the volume ratio: \(\frac{(3)^2 h_1}{(4)^2 h_2} = \frac{11}{16}\).

- Simplify to find: \(\frac{9 h_1}{16 h_2} = \frac{11}{16}\).

- Solve for the heights: \(\frac{h_1}{h_2} = \frac{11}{9}\).

Correct Answer: Option 1, 11 : 9