Can you solve this please

Let the radius , height and slant height  of the smaller cone be r,h and l

 And

 the same for the bigger cone be  R,H  and L.

Using similarity of triangles, we get that,

r/R=h/H=l/L

We know that,

 the CSA of the remainder is 8/9 of the CSA of the whole cone.

So the CSA of the smaller cone must be 1/9 th of the CSA of the whole cone.

So,

So if the height of the small cone is x, then, height of the big cone will be 3x.

So the line segments into which the altitude of the cone gets divided will be  x and 2x (2x=3x-x)