Find the volume of the solid with the given base and cross sections:

The base is the region in Quadrant I bounded by the curve $y=\sqrt[\phantom{2}]{9-x^2},$ the $x-$axis, and the $y-$axis. The cross sections perpendicular to the $x-$axis are squares.

$($a$)$ Sketch the solid and an example slice.

$($b$)$ Set up an integral to calculate the volume of this solid. Then evaluate this integral by hand. Find an exact answer $($no decimals$).$