## 91. Math Puzzle 12/72

In a cylindrical container filled with water to a height of $h=1.2 \mathrm{~m}$, a cylindrical submersible with a diameter of $d_{2}=30 \mathrm{~cm}$ is lowered to the bottom, causing the water level to rise by $\Delta h=4 \mathrm{~cm}$. How many liters of water are in the container?
If $d_{1}$ is the diameter of the cylinder, then

$$
\begin{gathered}
\frac{d_{1}^{2} \pi h}{4}=\frac{\left(d_{1}^{2}-d_{2}^{2}\right) \pi(h+\Delta h)}{4} \\
d_{1}=d_{2} \sqrt{\frac{h+\Delta h}{\Delta h}} \rightarrow V=\frac{d_{2}^{2}(h+\Delta h) \pi h}{4 \Delta h} \approx 2.63
\end{gathered}
$$

The container contains $2.63 \mathrm{~m}^{3}$ of water.