Rotations of Functions

So I am in BC Calc in my high school and we started rotations of functions. Now, the way i see it, a cylinder should be able to be evaluated to a rectangular prism, with r=l, and h=h, and then seeing as a full rotation is 2PI w=2PI. But it doesn't work for the rectangle. Can Anyone tell me where I've gone wrong?

I know shell method...
If you cut the cylinder along the line that marks the radius, and then an infinitely small distance away you cut again, making a rectangular prism that is the (integral of the rectangle)*x as x->0. Now you do that around the cylinder and make an infinite number of infinitely small cuts. Or at least as n->infinity, now you stack the rectangles on top of each other. That means, you would have the original rectangle(l*h) with an unknown width, but seeing as a full rotation in radians is 2π you can assume that the infinitely small widths you cut from the cylinder=2π when combined.
So then. l*w*2π should equal the same area of the cylinder, but it doesn't.