TITLE: Looking for an interesting problem/riddle involving triple integrals.
QUESTION [17 upvotes]: Does anyone know some good problem in real analysis, the solution of which involves triple integrals, and which is suitable for second semester Analysis students?
Thanks!

REPLY [2 votes]: This riddle is better phrased in term of double integral but can work for cubes instead of rectangles.
Here is the riddle: Call a rectangle integral if the length of (at least) one of its edges is an integer.
Prove that a rectangle that can be tessellate by integral  rectangles if also integral rectangle.
It is a huge hint to say that it has something to do with double integral so you may want to avoid it in the beginning.