Have you heard of discs vs. cylinders?

... Only if you are confined to discs (or 'washers')... where you rotate each Riemman strip around the axis perpendicular to the strip, e.g. you rotate a vertical strip (whose top and bottom values are in terms of x) around the x axis. Giving you a disc (in this case, but more generally a washer). Rotate the same vertical strip around the y axis instead and what do you get?

Solid of revolution - Wikipedia, the free encyclopedia