The ratio of volumes of two cones is 4:5 and the ratio of the radii of their bases is 2:3. Find the ratio of their vertical heights.

Explanation

To find the ratio of the vertical heights of two cones given the ratio of their volumes and the ratio of the radii of their bases, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Volume Formula for a Cone**:
The volume \( V \) of a cone is given by the formula:
\[
V = \frac{1}{3} \pi r^2 h
...