Question

A cone,a hemisphere and a cylinder stand on equal bases and have the same height.Show their ratio of volume

Answer 1

All stands on same base, means all have same radii.
Height of hemisphere, h = radius = r
Height of cone = height of cylinder = h =r
now. volume of cone = (1/3)πr²h
volume of hemisphere= (2/3)πr³ =  [∵r=h ]
volume of cylinder= πr²h = (3/3)πr²h
ratio,
cone:hemisphere:cylinder = [(1/3)πr²h]:[(2/3)πr²h]:[(3/3)πr²h]
                                          = 1:2:3

Answer 2

Volume of hemisphere= (2/3)πr³. As r=h, Volume of hemisphere= (2/3)πr²h Volume of cylinder= πr²h = (3/3)πr²h. Volume of cone = 1/3 πr²h. ratio of their respective volumes, volume of cone: volume of hemisphere:volume of cylinder = 1/3 πr²h: 2/3 πr²h: 3/3 πr²h. =} 1:2:3