Why hydrostatic paradox is a paradox? Someone could have simply told the student that pressure in a container is independent of the shape of container or area of cross section. Why give it the name “Hydrostatic Paradox”? What is the paradox here? Can some explain the reason behind this nomenclature?
 A: 
Why give a name Hydrostatic Paradox? What is the paradox here?

Consider two fluid filled vessels, one cylindrical and the other conical, with the same height and the same base area. The pressure at the bottom of the two vessels is the same because the height is the same, and because the base area is the same the force at the base is also the same. 
The paradox arises because the weight is different. The fluid in the conical vessel weighs much less than the fluid in the cylindrical vessel. So how can a lower mass produce the same force? This would not happen with a cylindrical and a conical solid. 
That is a surprising result that requires the student to think carefully about the pressure from the walls of the container. Apparently any surprising result that requires a student to think carefully can be called a paradox. 
A: The definition of Paradox refers to a statement that appears to be absurd or unreasonable, and yet with investigation and research it is proven to be correct. Since the fact that the pressure of a fluid depends on only the height of the fluid and not with the geometry of the container is rather unusual to many people who haven't come across this theory before, it can be considered to be a paradox.
