A solid $S$ has the following volume.

${\displaystyle \underset{0}{\overset{\sqrt[\phantom{2}]{14}}{}}}2(y+13)(14-y^2)dy$

If $S$ is a solid of revolution, how was $S$ obtained?

One way of obtaining $S$ is by rotating the region enclosed by $y=0,x=0,$ and $x=,.$ Another way to obtain $S$ is by rotating the region enclosed by $x=,x=14,$ and $y=0.$ Both enclosed regions are rotated about the line$($y$=13,$y$=-13,$y$=14$or y$=-14)$ using cylindrical shells.