Let $\backslash ($ S $\backslash )$ be the solid obtained by rotating the region shown in the figure below about the $\backslash ($ y $\backslash )-$axis.

Sketch the solid.

What are the circumference $\backslash ($ c $\backslash )$ and height $\backslash ($ h $\backslash )$ of a typical cylindrical shell?

$\backslash [$

c$($x$)=$

$\backslash ]$

$\backslash [$

h$($x$)=$

$\backslash ]$

Use the method of cylindrical shells to find the volume $\backslash ($ V $\backslash )$ of $\backslash ($ S $\backslash ).$

Do you think this method is preferable to using washers? Explain your reasoning.