A surface of revolution is a surface in Euclidean space created by rotating a curve around a straight line in its plane, known as the axis . Examples of surfaces generated by a straight line are cylindrical and conical surfaces when the line is co-planar with the axis, as well as hyperboloids of one sheet when the line is skew to the axis. A circle that is rotated about a diameter generates a sphere, and if the circle is rotated about a co-planar axis other than the diameter it generates a torus.

## Surface of Revolution

A portion of the curve

If the curve is described by the parametric functions

provided that

If the curve is described by the function

for revolution around the

for revolution around the

## Example

The spherical surface with a radius