Tennis balls are packed into a square box 23cm on one side. The tennis balls can be touching, but they can't be compressed. (1in=2.54cm, Height of a tennis ball is 2.6 in). The remaining space is filled with packing beads. How many tennis balls can be packed into the box? What is the volume occupied by the packing beads? What percentage of the volume of the box is filled with tennis balls? beads?

Question

Mathematics

Paul White

Today, 00:18

Tennis balls are packed into a square box 23cm on one side. The tennis balls can be touching, but they can't be compressed. (1in=2.54cm, Height of a tennis ball is 2.6 in). The remaining space is filled with packing beads. How many tennis balls can be packed into the box? What is the volume occupied by the packing beads? What percentage of the volume of the box is filled with tennis balls? beads?

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Sarai Juarez · Answer 1

The problem stats you cannot compress the balls; so you can not round up. You must round down. That means 4 x4 x4. There will be 16 balls per layer and 4 layers. So 48 balls.

The volume of the box is 12%5E3 inches.

You are told the diameter of a ball is 2.5 inches. So the radius of a ball is 1.25 inches

The volume of each ball is %284%2F3%29pi%2Ar%5E3

Subtract the volume of 16 balls from the volume of the box to get the volume of the packing bead material

To get the percentage of beads to box, divide the bead volume by the box volume and multiply by 100%