When we do volumes of solids of revolution, we're basically taking cross-sections of circles.
Draw the line y = 2 - x. Revolve that line 360 degrees around the x-axis and you'll get a cone. Now cut that cone into infinitely small sections. What you're left with is an infinite number of circles (two-dimensional, because we've split the cone infinitely).
If you examine each of those circles, you'll notice that they have a radius equivalent to the value of f(x). Like, at the base of the cone, you'd have a circle with area f(0) or 2 - 0 or 2. And at the tip, f(2) or 0.
So, if the function f(x) represents our radius at any given point for that solid, than if we integrate from 0 to 2, we'll be expanding f(x) over an infinite span of dx. Basically saying, we get infinite circles from 0 to 2 (we meaning we reverse to "cutting"). This, in essence, is no more than adding an extra dimension (the 3rd) to our two-dimensional circle.