Definition:Surface of Revolution
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Let $F$ be a plane figure.
Let $F$ be rotated one full turn about $L$ in $3$-dimensional space.
The usual scenario is that:
- $(1): \quad$ one of the sides of $F$ is a straight line coincident with $L$
- $(2): \quad$ $L$ itself is aligned with one of the coordinate axes, usually the $x$-axis in a cartesian plane
- $(3): \quad$ Two other sides of $F$ are also straight lines, perpendicular to $L$
- $(4): \quad$ The remaining side (or sides) of $F$ are curved and described by means of a real function.
The above diagram shows a typical surface of revolution.
$FECD$ illustrates the disposition of $ABCD$ part way round.