Four identical balls are stacked one above another inside a closed cylindrical tin. Each ball touches the curved wall, the top and bottom balls touch the lids, and the four together fill the tin's height exactly. What fraction of the tin is empty space?

Let each ball have radius $r$. The tin then has radius $r$ and height $8r$. The balls take up 4 × (4/3)π$r^3=(16/3)$π$r^3$ and the tin holds π$r^2(8r)=8$π$r^3$, so the balls fill (16/3)/8 = 2/3 of it and 1/3 is empty. The answer does not depend on how many balls are stacked — one ball in a snug tin leaves the same 1/3 empty. (2/3 is the filled part, the opposite of what is asked; 1/2 guesses that round things fill about half; 1/4 misreads the four balls as filling three quarters.)