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

In the equation of the function shown and everywhere else in this question use the values $\backslash ($ a$=6\backslash )$ and $\backslash ($ b$=1\backslash ).$

Sketch a typical approximating shell:

What are the circumference $\backslash ($ c $\backslash )$ and height $\backslash ($ h $\backslash )$ of this typical shell, in terms of its $\backslash ($ x $\backslash )-$coordinate?

$\backslash [$

c$($x$)=$

$\backslash ]$

$\backslash [$

h$($x$)=$

$\backslash ]$

Use shells to compute the volume $\backslash ($ V $\backslash )$ of $\backslash ($ S $\backslash ).$

$\backslash [$

V$=$

$\backslash ]$