$(2)$ Consider the disk bounded by the circle $\backslash ($ x$^\{2\}+$y$^\{2\}=$A$^\{2\}\backslash ),$ where $\backslash ($ A$>0\backslash )$ is a constant. If this disk is rotated about the line $\backslash ($ x$=$A $\backslash ),$ the resulting solid is sometimes called a pinched sphere.

$($a$)(2$ points$)$ Express the volume of the pinched sphere as an integral with respect to $\backslash ($ x $\backslash )($but do not evaluate it$).$

$($b$)(2$ points$)$ Express the volume of the pinched sphere as an integral with respect to $\backslash ($ y $\backslash )($but do not evaluate it$).$

$($c$)(2$ points$)$ Which integral would you rather work with? Evaluate whichever you choose.