OME 1967 Problem 4
There is a bottle with a flat and circular bottom, closed and partially filled of wine, so that its level does not exceed the cylindrical part. Discuss in which cases the capacity of the bottle can be calculated without opening it, having only one double graduated decimeter; and if possible, describe how it would be calculated.
(Problem of the Italian Gara Mathematica).
Dataset text AI-MO AoPS. Quoted with source.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.