First off, whenever I see circles or spheres, I try, whenever possible, to put the origin at the center. That just makes computations easier, usually. As your thread title indicates, this is a volume of the solid of revolution. Let's say that the sphere is chopped off at some point on the x axis. In other words, the sphere is "on its side", so to speak. This makes the integral not have to be pieced together in the variable of integration. Now, what shape, when revolved around the x axis, gives you a sphere? Can you find the equation of that shape? Now use the Calc II method: chop up your problem into little bits, solve the problem there, and integrate to find the answer.