Cube-shaped container

The cube-shaped container has a height of 52 cm and a square base. The container was filled to the brim with water, and then we immersed a metal cube in it, which caused 2.7 l of water to flow out of the container. After removing the cube from the water, the water level in the container dropped by 12 cm. How much l of water remained in the container?

Correct answer:

V =  9 l

Step-by-step explanation:

$$\begin{gathered} h=52\text{cm}\to \text{dm}=52:10\text{dm}=5.2\text{dm} \\ {V}_1=2.7\text{l}\to {\text{dm}}^3=2.7\cdot 1{\text{dm}}^3=2.7{\text{dm}}^3 \\ {h}_2=12\text{cm}\to \text{dm}=12:10\text{dm}=1.2\text{dm} \\ {V}_1=h_2\cdot S \\ S=V_1/h_2=2.7/1.2=\frac{9}{4}=2.25{\text{dm}}^2 \\ {V}_2=S\cdot h=2.25\cdot 5.2=\frac{117}{10}=11.7\text{l} \\ V=V_2-V_1=11.7-2.7=9\text{l} \end{gathered}$$

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