I have a somewhat interesting problem. Assume one has a tower of cannonballs, or spheres as pictured below
As in you have a tower of spheres where the first layer has $1$ cannonball, the next layer has $3$ cannonballs, and the $n$th layer has $n(n+1)/2$ cannonballs. Every ball is identical and has a radius of $r$. Now the problem is.
What is the smallest tetrahedron that can enclose this pyramid?
I gave it a few attempts, but they all turned out to be futile.