How to find height of two objects stacked at an angle

Question

Consider the following situation: If there are two balls of diameter 50mm and 60mm stacked inside a tube with internal diameter of 60mm. If the smaller ball is stacked on the big ball, it is easy to see that the height of the stacked balls will not be 110mm because the small ball will fall to one side. How can you determine the height of the stacked balls?

Answer 1

In the following figure it is clearly shown that $55^2=5^2+x^2$, that is, $x=\sqrt{55^2-25}$:

So the top of the smaller ball is at $25+30+x=25+30+\sqrt{55^2-25}\approx 104.8$.