1. The problem statement, all variables and given/known data Bounded by the cylinders x2 + y2 = r2 and y2 + z2 = r2 We're supposed to stick to double integrals as triple integrals are taught in a later section. 3. The attempt at a solution Edit: Alright, I think I go to the right answer. x = sqrt(r2 - y2) z = sqrt(r[SUP2[/SUP] - y2) The bounds are 0 < y < r and 0 < x < sqrt(r2 - y2) So I get: integrate integrate sqrt(r2 - y2) dx from 0 to sqrt(r2 - y2) dy from 0 to r The first integral goes to: sqrt(r2 - y2) * x from 0 to sqrt(r2 - y2) = (r2 - y2) The second integral then makes it: r2 * y - 1/3 * y3 from 0 to r which gives us: 2/3 * r3 However, you're supposed to throw in an 8 at the beginning to times everything by (why?) so you get: 16/3 * r3 So, my questions: Was my edited solution correct and why are you supposed to multiple the entire double integral by 8.