The essential concept here is similar triangles.
In the diagram above I have let r be the radius of the circle formed by the water surface. The triangles PQR and PTS are similar and hence
|QR|/|RP| = |TS|/|SP| that is 8/20 = r/x
r = 2/5 x
The volume of a cone of radius r and height h is
V = 1/3 r2 h
and hence the volume of water in your cone is
V = 1/3 r2 x = 1/3 ( 2/5 x)2 x = 4/75 x3