Explanation:

- The volumes of two cones are equal, and their heights are in the ratio 4:9.

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

- Since the volumes are equal, we have: \(r_1^2 \cdot h_1 = r_2^2 \cdot h_2\).

- Given the ratio of heights is \(h_1 : h_2 = 4 : 9\), then \(h_1 = 4k\) and \(h_2 = 9k\).

- Substituting into the volume equation: \(r_1^2 \cdot 4k = r_2^2 \cdot 9k\).

- Simplifying gives: \(r_1^2 : r_2^2 = 9 : 4\).

- Therefore, the ratio of the radii, \(r_1 : r_2\), is \(3 : 2\).

3 : 2

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