They want a new region in the plane, different from the old one, so that if you revolve the new region about the x-axis, you get the exact same cone as when you revolved the old region about the x-axis.

This is one of those problems that you have to think about a while, then say "aha!" and wonder why you had to think about it so long.

I think I can give you a hint without giving you the answer: If you add area to your region in quadrants II, III, or IV, you will add volume to the cone, so that's something you can't do.

- Hollywood