I'm having difficulties on finding volumes.

Here's my problem: The area bounded by the curves y = x + 2 and y = x^2 revolves about y = 4. What is the resulting volume?

How do I set this up? What's the radius function and height function? (I'm trying to use the shell method.)

I thought the radius function would be (4 - y) and the height function (y^0.5 - y + 2). But this doesn't seem to work.

And what if that area bounded revolved around the x-axis instead? How do I set that up?

I know how to use the disk method here, but I'm at a loss to the set up with the shell method.

Thanks for the help! I guess I'm not just "seeing" how these things work. That's why I don't know how to set them up.