Question

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Find the ratio of their volumes>

Answer 1

volume of cone - pi*r^2*h/3
volume of hemisphere -2/3*pi*r
volume of cylinder -pi*r^2h

ratio :-

volume of cone/volume of hemisphere/volume of cylinder
(pi*r^2*h/3)/(2/3*pi*r)/(pi*r^2*h)
=(r^2*h/3)/(2/3*r)/(r^2*h)
=(r*h/3)/(2/3)/(r*h)
=(r*h)/(2)/(3r*h)
=(r)/(2/h)/(3r)
=(1)/(2r/h)/(3)

then ratio will be ,
1:2r/h:3