$19.$ Consider the lines $\backslash ($ y$=16-$x$,$ y$=3$ x$+12\backslash ),$ and $\backslash ($ x$=0\backslash ).$

$($a$)$ Sketch the region enclosed by the three lines.

$($b$)$ Describe the cross$-$sections perpendicular to the $\backslash ($ x $\backslash )-$axis formed by rotating the region in part $($a$)$ about the $\backslash ($ x $\backslash )-$axis.

$($c$)$ Using your answer from $($b$),$ find the volume of the solid of revolution. Which method did you use $($disks$/$washers or cylindrical shells$)?$

$($d$)$ Repeat the problem using the method of cylindrical shells. Which variable will you integrate with respect to$?$ Your answer for the volume should remain the same.