$(9$ points$)$ The region $R$ enclosed by the graphs of $x=f(y)$ and $x=g(y)$ is given in the graphic

below. You may assume that the $x$ and $y$ bounds are as labeled on the graph.

$($a$)$ Set up$,$ do not evaluate, an integral for the volume obtained by rotating the region about

the line $x=8.$ You must state the method you are using.

Method:

Volume:

$($b$)$ Set up$,$ do not evaluate, an integral for the volume obtained by rotating the region about

the line $y=-1.$ You must state the method you are using.

Method:

Volume:

$($c$)$ Set up$,$ do not evaluate, an integral for the volume of the solid whose base is the region $R$

and every cross$-$section perpendicular to the $y-$axis is a triangle with equal base and height,

where the base of the triangle lies on $R.$