A surface of revolution is a surface generated by revolving a plane
curve *C* about a line *L* lying in the same plane as the
curve. The line *L* is called the *axis of revolution*

For the construction of this surface let *L* be the
*z*-axis. In order to construct a surface of revolution using a
parametric equation, it is important to first understand how a circle
is constructed in the plane since the surface is made up of a series
of circles at various heights. That is, if one slices the surface
with a plane that is parallel to the *xy*-plane, the intersection
is a circle. The parametric equation for a circle of radius 1 in the
*xy*-plane is *x*(*u*), *y*(*u*)) =
(cos*u*, sin*u*)__<__ *u*
__<__ 2pi*r*, the equation is *u*) =
(*r*cos*u*, *r*sin*u*)

In a surface of revolution, the radius may be different at each
height, so if the radius at height *v* is *r*(*v*),
then the equation of the surface is

where __<__ *u*__<__ 2pi

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