Q24 of 70 Page 21

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 right circular cone = (1/3)πr2h


Given, cone and a hemisphere have equal bases and equal volume


Height of a hemisphere is the radius and equal bases implies equal base radius.


(2/3)πr3 = (1/3)πr2h


⇒ r : h = 1 : 2


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