Explanation:

- The volume of a cone is given by the formula: \(\frac{1}{3} \pi r^2 h\).

- The volume of a cylinder is given by the formula: \(\pi r^2 h\).

- The volume ratio of the cone to the cylinder is given as 8:9.

- Therefore, \(\frac{1}{3} \pi r_1^2 h_1 : \pi r_2^2 h_2 = 8:9\).

- Heights are in the ratio 2:3, so \(h_1:h_2 = 2:3\).

- Substituting height ratio and simplifying, the formula becomes: \(\frac{r_1^2}{r_2^2} = \frac{8 \times 3}{9 \times 2} = \frac{4}{3}\).

- Therefore, the ratio of the radii \(r_1:r_2\) is the square root of \(\frac{4}{3}\), which simplifies to \(2:1\).

- Correct Answer: Option 3 - 2:1