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MathNet 2018-part-03 — 181 problems (EN–VI) Question 60

Math Olympiad Vault · MathNet 2018-part-03 — 181 problems (EN–VI)

Question 60

A cone-shaped bottle rests on its base. It is filled with water until the level of the liquid reaches $8$ centimetres, measured vertically, below the vertex of the cone. If the bottle is now turned upside down, without changing the amount of water inside it, the space that remains empty in the upper part of the inverted cone is $2$ centimetres high.
How tall is the bottle?