Cone Pressure Force

There is a body of fluid filling the space below the plane $z = 0$ . The fluid has volume-mass-density $\rho = 1$ . There is a solid right circular cone of radius $1$ whose vertex is at $(x,y,z) = (0,0,0)$ . The center of the cone's circular base is at $(x,y,z) = (1,0,-1)$ . The ambient gravitational acceleration is $10$ in the negative $z$ direction.

The surface of the cone has two parts: The circular base $(S_1)$ , and the remaining portion $(S_2)$ . Determine the magnitude of the force exerted by the fluid on $S_2$ .

Note:
1) There is no pressure at $z = 0$
2) The cone displaces fluid from the volume it occupies