I don't know the name of the solid built on a sphere's surface. I mean, given a sphere of radius r1, create another sphere with the same origin and radius $r_2$, with $r_2 > r_1$. I'm interested in the solid that results when you "subtract" the first sphere from the second one.
If we were in 2D the object would be a ring.
It is called a spherical shell.