I had trouble finding this information online, so I'm going to post it here to make it easier for others to find.The geometric name for the shape of a Hula Hoop or a smoke ring (which are hollow) is a torus. If the shape is solid, like a donut or a ring, it's called a toroid.
Put another way, a torus is the surface area of a toroid, and a toroid is the shape enclosed by a torus.
You might hear a geometry geek at a basketball game root for the players to "put the sphere through the toroid!" (and now you'll know what they mean.)
