$(15$pts$)$ Consider ${\displaystyle \underset{-\sqrt[\phantom{2}]{3}}{\overset{\sqrt[\phantom{2}]{3}}{}}}{\displaystyle \underset{-\sqrt[\phantom{2}]{3-y^2}}{\overset{\sqrt[\phantom{2}]{3-y^2}}{}}}{\displaystyle \underset{1}{\overset{\sqrt[\phantom{2}]{4-x^2-y^2}}{}}}(x^2+y^2)dzdxdy$

$($a$)$ Convert to cylindrical coordinates, but do NOT evaluate it$.$ Use sketches to justify.

$($b$)$ Convert to spherical coordinates, but do NOT evaluate it$.$ Use sketches to justify.