how would I calculate how many ping pong balls fit into a cylinder?

Question

I want to make a lamp made of ping pong balls in a large glass vase and need to calculate the the required amount of ping pong balls

Answer 1

There is an extensive literature on sphere packing, but I'm not familiar with it. The section on irregular packing in the Wiki article suggests that you won't get a density of more than $64\%$. That is, the total volume of the ping pong balls will not exceed $64\%$ of the volume of the cylinder. So if $R,h$ are the radius and height of the cylinder, and $r$ is the radius of a ping pong ball ($r=20$ as I understand it) then$$ .64\frac{3R^2h}{4r^3}=.48\frac{R^2h}{r^3}$$ ought to be enough ping pong balls.