Question

If a cone is cut into two parts by a horizontal plane passing through the mid point of it's axis the ratio of their volumes

Answer 1

Answer:

If we cut a cone from midpoint then

use this concept .

let r is radius of above part and R is the radius of base of cone .

Let us suppose their heights h & h/2 .

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 of their volumes =1:7

Hope it helps! ! !