How is it possible calculate Volumes from Adding together Areas? You can't find the volume for a $2D$ object, but by finding the area of say a square $A$ and multiply by any height $H$ you get the volume of cube with base $A$ and height $H$. 
Here's my question. Is the volume of an object made of a very large amount of $2D$ surfaces stacked over each other? If yes, how is that possible? Since A $2D$ surface has thickness of $0$ isn't it like adding an infinite amount of zeroes and expecting to get a number that isn't zero?

I think this is just a matter of conceptualisation. But Calculus is better because it gives us the concept and the language to do the calculations.
Another way is instead of thinking that a 2D area has zero height, I would like to think that height is undefined in the 3rd dimension. Then when you multiply by the height, you give the physical object a 3rd dimension and the new definition is of a volume.
We need to consider the physical dimension or unit of measure that you are multiplying or "adding". For example,


*

*same dimension e.g. 1 unicorn + 1 unicorn = 2 unicorns;

*certain pre-requisites must be stated outside of the mathematical statement e.g. you cannot simply add density together normally without specifying you how do it physically; 

*adding generates a new dimension, as in area into volume.


So in the case of area multiply by height, you are not really stacking sheets of zero height paper, but rather "extruding" the paper.
