A solid $S$ has the following volume.

${\displaystyle \underset{0}{\overset{\sqrt[\phantom{2}]{10}}{}}}2(y+12)(10-y^2)dy$

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 $x=,x=10,$ and $y=0.$ Both enclosed regions are rotated about the line $$ using cylindrical shells.