Option : (A)
Volume of a hemisphere = \(\frac{2}{3}\)πr3
Volume of a right circular cone = \(\frac{1}{3}\)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 = \(\frac{1}{3}\)πr2h : \(\frac{2}{3}\)πr3 : πr2h
⇒ Ratio of volumes = r3 : 2r3 : 3r3
= 1 : 2 : 3