Volumes and Surfaces of Solids of Revolution
The body generated by the revolution of a plane area, about a fixed line lying in its own plane, is called a solid of revolution. On the other hand, the surface generated by the boundary of the plane area is called the surface of revolution. The fixed line, lying in the plane of plane area, about which the plane area revolves is called the axis of revolution. The section of a solid of revolution by a plane, perpendicular to the axis of revolution, is a circle having its center on the axis of revolution.
11.1 VOLUME OF THE SOLID OF REVOLUTION (CARTESIAN EQUATIONS)
(A) Revolution About x-axis: Let AB be the arc of the curve y = f (x) lying between the ordinates x = a and x = b. We assume that