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A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.
Volume of a hemisphere = (2/3)πr3
Volume of a cone = (1/3)πr2h
Given, cone and a hemisphere have equal bases which implies they have the same radius.
Height of the hemisphere is its radius.
Let the base radius be ‘r’ and the height of cone be ‘h’.
Given, cone and hemisphere have equal volume.
(2/3)πr3 = (1/3)πr2h
⇒ h : r = 2 : 1