Question

A cylinder is circumscribed about a hemisphere and a cone is inscribed in the cylinder so as to have its vertex at the centre of one end and the other end as it's base. The volume of the cylinder, hemisphere and the cone are respectively in the ratio of :

Answer 1

let the radius of all the figures be r
since cylinder is circumscribed in hemisphere and so the cone therefore height of both cone and cylinder =r
volume of hemisphere (VH)=2/3Πr^3
volume of cylinder (VCY)=Πr^2h=Πr^3
volume of cone (VCO)=1/3Πr^2h=1/3Πr^3
therefore VH:VCY:VCO=2/3:1:1/3=2:3:1