## 4. Submerged Bodies

Marta is playing with models of geometric bodies by submerging them in water in a container shaped like a cube. If she places a cube and a cylinder in the container, the water level rises $5 \mathrm{~cm}$ more than if she only places a pyramid. If she places a cube and a pyramid in the container, the water level rises $10 \mathrm{~cm}$ more than if she only places a cylinder. When the pyramid and the cylinder are in the container, the water level is the same as when only the cube is in it. By how many millimeters will the water level rise if Marta places the cube, the cylinder, and the pyramid in the container?

## Result: 150
Solution. Let $k$ be the increase in water level due to placing the cube in the container (in cm), and similarly $v$ for the cylinder and $p$ for the pyramid. According to the conditions of the problem, we have:

$$
\begin{aligned}
& k+v=p+5 \\
& k+p=v+10 \\
& p+v=k
\end{aligned}
$$

If we add all three equations, we get

$$
k+v+k+p+p+v=p+15+v+k
$$

If we subtract the same addends $p, v$, and $k$ from both sides, we get

$$
k+v+p=15
$$

Therefore, if Marta places the cube, the cylinder, and the pyramid in the container, the water level will rise by $15 \mathrm{~cm}$ or $150 \mathrm{~mm}$.

Note: By solving the system, we can obtain $k=7.5, v=2.5$, and $p=5$.