Tennis Ball Can Volume

In a can of tennis balls that is exactly three balls high, which is greater, the volume of the balls or the volume of the air around the balls? (Disregard the thickness of the balls.)


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Here’s a cross-section of the can with 3 balls in it.
The volume of one tennis ball is 4/3 pir3, so all three are 4pir3.
The volume of the cylinder is pir2 · 6r = 6pir3.
The volume of air around the balls, thus is 2pir3.

Thus the volume of air is only half the volume of the balls.


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