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Volume of a hemisphere = (2/3)πr³

Volume of a right circular cone = (1/3)πr²h

Volume of a cylinder = πr²h

Given, a cone, a hemisphere and a cylinder stand on equal bases and have the same height.

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

Thus, height of cone = height of cylinder = base radius = r

Ratio of volumes = (1/3)πr²h : (2/3)πr³ : πr²h

⇒ Ratio of volumes = r³ : 2r³ : 3r³ = 1 : 2 : 3