How to do a 'swept volume' of a 3D shape

I have a model that is in essence a rectangle with and elliptical surface on one side (this is representative of a flat plate that rotates a specified amount of degrees in the X axis). I am now wanting to rotate this 360 degrees (along the Y-Axis, ROTATE_CENTER, shown below)to create a full on 360 degree swept volume so I can understand the full volume this will occupy in the real world. Any suggestions on how to achieve this?