$[9-11]$ Consider the graph of the function f given by $\backslash ($ f$($x$)=\backslash$frac$\{1\}\{$x$+2\}\backslash )$ for $\backslash ($ x $\backslash$geq $0\backslash ).$Let $\backslash ($ R $\backslash )$ be the region bounded by the graph of $\backslash ($ f $\backslash ),$ the $\backslash ($ x $\backslash )-$ and $\backslash ($ y $\backslash )-$axes, and the vertical line $\backslash ($ x$=$k $\backslash ),$ where $\backslash ($ k $\backslash$geq $0\backslash )$

$9.$ Find the area of the region R$,$ in terms of k $.$

$10.$ Find the volume of the solid generated when the region $\backslash ($ R $\backslash )$ is revolved about the x $-$axis, in terms of k $.$

$11.$ Let S be the unbounded region in the first quadrant to the right of the vertical line $\backslash ($ x$=$k $\backslash )$ and below the graph of f$.$ Find all values of $\backslash ($ k $\backslash )$ such that the volume of the solid generated when $\backslash ($ S $\backslash )$ is revolved about the x $-$axis is equal to the volume of the solid found in $\backslash$#$10.$