Mr. Celer had two identical tanks in the shape of a quadrilateral prism with a square base in his garden. Together, he had 300 liters of water in both. In the first tank, the water formed a perfect cube and filled $62.5\%$ of the tank, while in the second tank, there was 50 liters more water. What were the dimensions of Mr. Celer's tanks?

(L. Hozová)
Let the length of the edge of the square base be denoted by $a$ and the height of the prism by $v$. Both quantities are expressed in $\mathrm{dm}$; the volume of the tank in liters is given by $V=a^{2} \cdot v$. The volume of water in the first tank was $a^{3}$, in the second tank $a^{3}+50$, and together 300. Therefore, we have

$$
a^{3}+\left(a^{3}+50\right)=300,
$$

from which we can easily express $a^{3}=125$ and $a=5(\mathrm{dm})$.

In the first tank, there were 125 liters of water, which represented $62.5\%$ of the total volume $V$. Therefore,

$$
125=\frac{62.5}{100} \cdot V
$$

from which we can express $V=125 \cdot \frac{100}{62.5}=2 \cdot 100=200\left(\mathrm{dm}^{3}\right)$. Using the relationship $V=a^{2} \cdot v$, we can now calculate the last unknown:

$$
v=\frac{V}{a^{2}}=\frac{200}{25}=8(\mathrm{dm})
$$

The dimensions of each tank were $5 \mathrm{dm} \times 5 \mathrm{dm} \times 8 \mathrm{dm}$.

Evaluation. 2 points for expressing the edge of the base; 2 points for expressing the volume of the tank; 2 points for expressing the height.