Deciliters - balls

We placed 10 layers of 100 balls with a diameter of 1 cm in a cube-shaped aquarium with an inner edge length of 10 cm. How many deciliters of water could still fit in the aquarium?

Final Answer:

V =  4.8 dl

Step-by-step explanation:

$$\begin{gathered} a=10\text{cm}\to \text{dm}=10:10\text{dm}=1\text{dm} \\ n=10\cdot 100=1000 \\ d=1\text{cm}\to \text{dm}=1:10\text{dm}=0.1\text{dm} \\ r=d/2=0.1/2=\frac{1}{20}=0.05\text{dm} \\ {V}_1=a^3=1^3=1\text{l} \\ {V}_2=n\cdot \frac{4}{3}\cdot \pi \cdot r^3=1000\cdot \frac{4}{3}\cdot 3.1416\cdot 0.05^3\doteq 0.5236\text{l} \\ {V}_3=V_1-V_2=1-0.5236\doteq 0.4764\text{l} \\ V=10\cdot V_3=10\cdot 0.4764=4.8\text{dl} \end{gathered}$$

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