1. The problem statement, all variables and given/known data x=1+(y-2)^2, x=2. Rotating about the x-axis 2. Relevant equations Volume=(2∏y)(1+(y-2)2(Δy) Limits of integration would be from 1 to 3 2∏∫(y)(1+(y-2)2dy 2∏∫y3-4y2+5y dy 3. The attempt at a solution 2∏[y4/4-4y3/3+5y2/2] Plug in the limits and I get 32∏/3. The answer is 16∏/3. It works if for the circumference you use 2∏ instead of 2∏y.