Question

A cone and a hemisphere have equal base and equal volumes, find the ratio of their heights

Answer 1

base of cone= base of hemisphere=r (say)
volume of cone = volume of hemisphere
1/3 πr^2h = 2/3 πr^2H
1/3h = 2/3 H
now, h/H = (2/3)/(1/3)
h/H= 2/1
h:H = 2:1
where h is the height of cone
and. H is the height of hemisphere...

hope it is clear...