A Hollow cone is cut by a plane parallel to the base and upper portion is removed. If the curved surface of the remainder is 8/9 of the curved surface of the whole cone; find the ration of the line-segment into which the cone's altitude is divided by the plane.

Explanation

Assume that the ratio of the altitude of the bigger and the smaller cone be` k:1`.

Let R and r be the radii of the bigger and the smaller cone respectively.

Let H and h be the radii of the height of the bigger abd the smaller cone respectively.

Consider th e similar triangles` /_\ AGC & /_\ AFE`,

By the property of similarity, we have,

`AG/AF = GC/FE`

`h/H = r/R = 1/k`, where k is some constant.

curved surface area of bigger cone` = pi RL`,

...