Kuba found three boxes in the basement, each in the shape of a rectangular prism with a square base. The first one was twice as high as the second one. The second one was 1.5 times wider than the first one. The third one was three times higher than the first one and twice as narrow as the first one. In what ratio are the volumes of the boxes?

(M. Raabová)
We will enter the data into a clear table:

| box | length of the base edge | height |
| :--- | :---: | :---: |
| first | $a_{1}$ | $v_{1}=2 v_{2}$ |
| second | $a_{2}=1.5 a_{1}$ | $v_{2}$ |
| third | $a_{3}=0.5 a_{1}$ | $v_{3}=3 v_{1}$ |

We will express the dimensions of the containers using $a_{3}$ and $v_{2}$:

| box | length of the base edge | height |
| :--- | :---: | :---: |
| first | $a_{1}=2 a_{3}$ | $v_{1}=2 v_{2}$ |
| second | $a_{2}=3 a_{3}$ | $v_{2}$ |
| third | $a_{3}$ | $v_{3}=6 v_{2}$ |

Using these data, we will express the volumes of all the boxes:

$$
\begin{aligned}
\text { first container: } & V_{1}=\left(2 a_{3}\right)^{2} \cdot 2 v_{2}=8 a_{3}^{2} v_{2}, \\
\text { second container: } & V_{2}=\left(3 a_{3}\right)^{2} \cdot v_{2}=9 a_{3}^{2} v_{2}, \\
\text { third container: } & V_{3}=a_{3}^{2} \cdot 6 v_{2}=6 a_{3}^{2} v_{2} .
\end{aligned}
$$

It is evident that the volumes of the containers are in the ratio $8: 9: 6$.