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Part of 2018 ITAMO

Problems(1)

ITAMO problem 1

Source: ITAMO 2018

5/9/2018
1.1.A bottle in the shape of a cone lies on its base. Water is poured into the bottle until its level reaches a distance of 8 centimeters from the vertex of the cone (measured vertically). We now turn the bottle upside down without changing the amount of water it contains; This leaves an empty space in the upper part of the cone that is 2 centimeters high.
Find the height of the bottle.
geometry3D geometry