Only part D Find the volume of the solid generated by revolving the region bounded by $y=4\sqrt[\phantom{2}]{x}$ and the lines $y=4\sqrt[\phantom{2}]{13}$ and $x=0$ about

a$.$ the $x-$axis.

b$.$ the $y-$axis.

c$.$ the line $y=4\sqrt[\phantom{2}]{13}.$

d$.$ the line $x=13.$

a$.$ The volume of the solid generated by revolving the region bounded by $y=4\sqrt[\phantom{2}]{x}$ and the lines $y=4\sqrt[\phantom{2}]{13}$ and $x=0$ about the $x-$axis is $1352$ cubic units.

$($Type an exact answer, using $$ as needed.$)$

b$.$ The volume of the solid generated by revolving the region bounded by $y=4\sqrt[\phantom{2}]{x}$ and the lines $y=4\sqrt[\phantom{2}]{13}$ and $x=0$ about the $y-$axis is $\frac{676\sqrt[\phantom{2}]{13}}{5}$ cubic units.

$($Type an exact answer, using $$ as needed.$)$

c$.$ The volume of the solid generated by revolving the region bounded by $y=4\sqrt[\phantom{2}]{x}$ and the lines $y=4\sqrt[\phantom{2}]{13}$ and $x=0$ about the line $y=4\sqrt[\phantom{2}]{13}$ is $\frac{1352}{3}$ cubic units.

$($Type an exa

d$.$ The volume of the solid generated by revolving the region bounded by $y=4\sqrt[\phantom{2}]{x}$ and the lines $y=4\sqrt[\phantom{2}]{13}$ and $x=0$ about the line $x=13$ is cubic units.

$($Type an exact answer, using $$ as needed.$)$