Suppose b > a > 0.
Consider a sphere of radius b, and a circular cylinder of radius a, both centered at the origin. Consider the solid ring formed by all the points which are both inside the sphere and outside the cylinder. Imagine boring a hole with a cylindrical drill, and punching it all the way through.
(a) Find the height h of the ring. You should express h in terms of a and b. Please accompany with a labeled sketch.
(b) Find the volume of the ring, in terms of a and b.
(c) Express the volume in terms of the height h of the ring only.