Cylinder cube water

We placed the largest possible lead cylinder inside a 1-litre cubic container. How many decilitres of water will now fit in the container?

Final Answer:

x =  2.146 dl

Step-by-step explanation:

$$\begin{gathered} V_1=1\text{l}\to {\text{dm}}^3=1\cdot 1{\text{dm}}^3=1{\text{dm}}^3 \\ {V}_1=a^3\text{dm} \\ a=\sqrt[3]{V_1}=\sqrt[3]{1}=1\text{dm} \\ r=a/2=1/2=\frac{1}{2}=0.5\text{dm} \\ {V}_2=\pi \cdot r^2\cdot a=3.1416\cdot 0.5^2\cdot 1\doteq 0.7854{\text{dm}}^3 \\ V=V_1-V_2=1-0.7854\doteq 0.2146{\text{dm}}^3 \\ x=10\cdot V=10\cdot 0.2146=2.146\text{dl} \end{gathered}$$

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