Three-quarters of volume

A cylindrical container is three-quarters full with six liters of water. We dip a cube-shaped body into the container, which sinks to the bottom. The length of the edge of the cube is 13 cm. Decide what happens to the sink after the cube is dipped.

Correct answer:

x = 0

Step-by-step explanation:

$$\begin{gathered} V_1=6\text{l}\to {\text{dm}}^3=6\cdot 1{\text{dm}}^3=6{\text{dm}}^3 \\ \frac{3}{4}\cdot V=V_1 \\ V=V_1\cdot \frac{4}{3}=6\cdot \frac{4}{3}=\frac{6\cdot 4}{3}=\frac{24}{3}=8{\text{dm}}^3 \\ a=13\text{cm}\to \text{dm}=13:10\text{dm}=1.3\text{dm} \\ {V}_2=a^3=1.3^3=2.197{\text{dm}}^3 \\ {V}_3=V-V_1=8-6=2{\text{dm}}^3 \\ {V}_2>V_3 \\ x=0 \end{gathered}$$

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