How many ping pong balls can fit in a typical-sized room without being crushed?

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SUMMARY

The discussion focuses on estimating the number of ping pong balls, each with a radius of 2 cm, that can fit into a typical room measuring 17 ft x 17 ft x 7 ft. The room's dimensions convert to approximately 518 cm x 518 cm x 213 cm. Two methods were explored: calculating the volume using cubic packing with 4 cm cubes and applying a spherical packing approach, which suggests a packing efficiency of about 70%. The conclusion emphasizes the need to determine an effective packing pattern for optimal results.

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Homework Statement


Estimate the number of ping pong balls (of radius 2cm) that would fit into a typical-sized room (without being crushed). A typical room is 17ft x 17ft x 7ft.


Homework Equations


none


The Attempt at a Solution


I tried a couple things:
1. After converting all dimensions to cm, I tried to see how many cubes of edge length 4cm would fit in the room.
2. I used a "spherical packing" method where I found the total volume of the room and multiplied it by .70.

Any help would be greatly appreciated :)
 
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What were the results of what you have tried?
 
4 cm spheres can be packed closer together than 4 cm cubes. You'll need to figure out a pattern for the packing.
 

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