Question

A cone and a hemisphere have equal bases and equal volumes. Find the ratio in their heights.

Solution

Let r be the radius of cone and hemisphere and let h be the height of the cone then  Volume of cone =13πr2h  ∵ Their volumes are equal, then 13πr2h=23πr3⇒13h=23⇒hr=23×31=21∴Ratio=2:1

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