What exactly is the shape of the cone? That is, what is the total height when the radius is 9 cm? The volume of a cone, of radius a and height h, is . You say that the volume is given by which leads me to the conclusion that the height is . With a= 9 cm, that gives or about 0.318 cm. I find that hard to believe!
If a cone has radius R and height H, then for any given height, h, above the vertex, the radius at that height is given by or . A circle with that radius has area and, if we think of it as a thin disk of height dh, volume . We can find the volume between two different height, and by integrating that:
So the distance from , at the vertex, to the height, where the volume is 1000 ml is . Once you have solved for that h, set it equal to and solve for the next .