Why are we able to calculate volume on a 2D graph When one is asked to rotate a plane across some line (with, say the shell method),  a 3D object is realized. However, since a standard graph involves only x and y, why are we able to calculate volume from a 2D graph. 
 A: We can not calculate a non-zero volume from a two-dimensional graph. 
Take a two-dimensional graph, either one you found somewhere or one you created. What non-zero volume does it define? None!
You get a positive volume only when you take some other steps such as rotating the graph around a line. Even then you cannot say what the volume is unless you know which line the graph is rotated around. 
When you do the shell method, what you’re actually measuring is the volume of each shell. In the limit as the shells' thickness goes to zero, all you need to know about each shell is its radius and length. You could measure those things anywhere on the shell, but it happens to be convenient to measure them where the shell intersects the original graph. 
But in any case, the only way a two-dimensional object can have anything to do with a non-zero volume is if you have a known relationship between the two-dimensional object and a three-dimensional object whose volume you are interested in. 
A: The answer is implicit in your question, and the key is in the rotation. When you rotate a plane region about some axis in that plane, all points of the region except those on the axis leave the plane -- in other words enter the third dimension. It is this that makes it possible. You can imagine this or draw a figure -- as the region sweeps out of its original plane, it always lies in one of a continuous "sequence" of planes, which generate some solid region in space.
In short, by rotating you lift it out of its initial plane.
