Balls

Ping-pong balls have a diameter of approximately 4 cm. It is sold in boxes of 9 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.

Correct answer:

x =  52.36 %

Step-by-step explanation:

$$\begin{gathered} x=100\cdot \frac{9\cdot V_1}{9\cdot V_2}=100\cdot \frac{V_1}{V_2} \\ x=100\cdot \frac{\frac{4}{3}\pi r^3}{(2r{)}^3} \\ x=\frac{4\cdot \pi \cdot 100}{3\cdot 8}=\frac{50\cdot \pi }{3} \\ x=52.36\% \end{gathered}$$

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