The question is about sphere like surfaces, like the hemispherical base of a cylinder as shown.
The cylinder is filled with fluid till the given height $h$, and the density of the fluid is $\rho$ and the system is static.I need to find the force due to pressure on the hemispherical portion at the base. I know that the pressure experienced by a ring of thickness, say, $dx$, if the area it contains is parallel to the top of the cylinder, will be equal throughout the ring. And also, the pressure in the hemispherical region changes from $\rho gh$ to $\rho g(h+r)$ (from the disk at the top to the infinitesimal one at the bottom).
(I've tried to find the Force by integrating $PdA$ over each ring, with their radii ranging from $R$ to $0$, and the pressure varying like I mentioned above, but that apparently is not the right way to do it.)