Before I ask my question, I would like to clarify that this is NOT a homework question. Rather I would like to clear up an issue with my intuition about fluid statics using this problem. Firstly, I feel like there can't be any pressure on the bottom of container C as if the container is a perfect triangle with sharp edges, there wouldn't be any perpendicular surface to have pressure, so how would I go about finding the pressure at the bottom of container C?
Secondly, I am unsure why and how changing the volume of the container would change the pressure at the bottom. I feel like these problems are arising due to my misunderstanding on how pressure works, hence I would like to clarify these gaps in my intuition. Thanks!
Note that the answer to part (a) is all 3 containers have the same pressure at the bottom (which I don't see why). The answer to part (b) is $A<B<C$ (which I don't see why either).
Best Answer
Your confusion is understandable! In Wikipedia, for example, pressure is defined as "Pressure (symbol: p or P) is the force applied perpendicular to the surface of an object per unit area over which that force is distributed."; and it is entirely natural to think that there is an intimate and necessary connection between "pressure" and a "surface".
However, that definition of pressure is inadequate. Pressure exists whether or not there is a surface to experience the forces of pressure. It is an aspect of the condition of the fluid at any and every point in the fluid; and it exists throughout the fluid.
The reason definitions of pressure mention surfaces is that one way to measure pressure is to introduce, for example, a piston whose front face (a surface) is exposed to the fluid pressure, and whose back face is exposed to vacuum. The force exerted by the fluid against the piston, divided by the area of the piston's face, is equal to the pressure in the fluid.
However, there are other ways to measure pressure that do not involve a surface at all. For example, if the fluid is a gas it is subject to the Ideal Gas Law. From the Ideal Gas Law, the pressure $P$ at any point can be determined by measuring the temperature and density of the gas.
Changing the volume of the container in your example does not affect the pressure at the bottom of the container, but any change in shape that changes the height of the fluid will change the pressure at the bottom because the pressure is proportional to the height of fluid above the bottom (if the fluid is incompressible like water).