1. The problem statement, all variables and given/known data The problem is that an ellipse (centered at origin) is revolved about y-axis. Now I have to find the volume of this swept region. But how do I go about using calculus? I have to derive it. 2. Relevant equations Volume of ellipsoid = 4/3*pi*abc (source wikipedia) Equation of ellipse: x^2/a^2 + y^2/b^2 = 1 3. The attempt at a solution integral(pi*a*b*dθ), limits 0 to pi. What is wrong with this? Now I know after searching that the volume is given by integral(pi*y^2*dx), limits -b to b, but how do you get this?