Balls

Ping-pong balls have a diameter of approximately 5.5 cm. It is sold in boxes of 8 pieces: each box has a cuboid shape with a square base. The balls touch the walls of the box.

Calculate what portion of the internal volume of the box is filled with balls.

Final Answer:

x =  52.36 %

Step-by-step explanation:

$$\begin{gathered} r=5.5\text{cm} \\ n=8 \\ x=100\cdot \frac{n{V}_1}{n{V}_2}=100\cdot \frac{V_1}{V_2} \\ x=100\cdot \frac{\frac{4}{3}\pi r{}^3}{(2r{)}^3} \\ x=100\cdot \frac{\frac{4}{3}\pi r{}^3}{8r^3} \\ x=100\cdot \frac{\frac{4}{3}\pi }{8} \\ x=100\cdot \frac{4\pi }{3\cdot 8} \\ x=100\cdot \frac{\pi }{3\cdot 2} \\ x=100\cdot \frac{\pi }{6}=100\cdot \frac{3.1416}{6}=52.36\% \end{gathered}$$

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