## 11

## 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