How many 20lb medicine balls can you fit in a 10x10x10 foot room?
Logical answers only please.
For a logical answer you need more information as the weight of the ball is not particularly relevant. If we assume a standard 14 inch diameter for these balls then you can do a calculation. Getting to the exact number is a tough problem because it depends on figuring out the most efficient way to stack the balls. I'll do a 'lower end" calculation and I suggest you then take this to the math section to see if they can improve on it.
The "lower end" would mean stacking the balls side by side with each layer directly on top of the prior layer. This way you can fit 8 balls in each dimension and thus your answer would be 8x8x8=512. Thus, you can fit AT LEAST 512 balls in the room.
As you can see, you may be able to fit more balls in by putting one layer's balls between those on the layer below so depending on the specifics of the room you probably can fit more than 512. We can also do a "higher end" calculation where we assume the balls keep their volume but their shape does not have to remain spherical. If we can jam them in to take up ALL the volume in the room we can fit a lot more balls in. The total room volume is 120 x 120 x 120 = 1,728,000 cu in. A ball with 14 in diameter has a volume of 4/3*3.14*7^3 = 1,436 cu in. Dividing you see you can get 1203 balls in the room. So that is our upper end of possibility but you would never achieve it unless the balls are perfectly malleable (essentially, liquid).
Finally, you can consider trick questions and nonconventional answers like..."well, first I let the air out of each ball...". In that case, you might fit more than 1203 balls.
I suspect you are looking for the best answer where the balls must remain spherical. I suggest you post this in the math section and make it clear you already know the "easy" 512 ball answer but you are looking for the optimized answer where the balls must keep their original shape.
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