Question

# A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Show that their volumes are in the ratio 1 : 2 : 3.

Solution

## ∵ Bases and heights of a cones hemisphere and a cylinder are equal Let r be the radius and h be their heights now volume of cone =13πr2h Volume of Hemisphere =23πr3  and volume of cylinder =πr2h  ∴ Ratio in thir volumes =13πr2h:23πr3:πr2h=13h:23r:h=13h:23h:h=13:23:1=1:2:3

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