Consider the function $f(x)=2(36+x^2{)}^{-\frac{1}{2}}$ and the region $R$ on the interval $0,8.$ See the figure to the right.

a$.$ Find the area of $R.$

b$.$ Find the volume of the solid generated when $R$ is revolved about the $x-$axis.

c$.$ Find the volume of the solid generated when R is revolved about the y $-$axis.

a$.$ The area of $R$ is $$ square units.

$($Type an exact answer.$)$

b$.$ The volume of the solid generated when R is revolved about the x $-$axis is $$ cubic units.

$($Type an exact answer in terms of $.)$

c$.$ The volume of the solid generated when $R$ is revolved about the $y-$axis is $$ cubic units.

$($Type an exact answer in terms of $.)$