Question

If a cone is cut into two parts by a horizontal plane passing through the mid point of its axis, find the ratio of the volumes of upper and lower part.

Answer 1

If we cut cone from midpoint thenuse similarly concept .

let r is radius of above part and R is the radius of base of cone .
R/r=h/(h/2)=2/1
R=2r
now
volume of cone =πR^2h
=π(2r)^2h=4πr^2h
volume of small cone =πr^2h/2
now,
volume of below part =4πr^2h-πr^2h/2
=7/2 πr^2h

now ratio = volume of above part/volume of below part
=(πr^2h/2)/(7/2πr^2h)=1/7
hence ratio =1:7