three triple integrals.

$($a$)$ The integral in spherical coordinates is ${\displaystyle \underset{0}{\overset{\phantom{}}{}}}{\displaystyle \underset{0}{\overset{\phantom{}}{}}}{\displaystyle \underset{\frac{4}{cos}}{\overset{\phantom{}}{}}}ddd$

$($Type exact answers, using $$ as needed$)$

$($Type exact answers, using $$ as needed$)$

$($b$)$ The integral in cylindrical coordinates is ${\displaystyle \underset{0}{\overset{\phantom{}}{}}}{\displaystyle \underset{0}{\overset{\phantom{}}{}}}{\displaystyle \underset{4}{\overset{\phantom{}}{}}}dzdrd$

$($Type exact answers, using $$ as needed.$)$

$($c$)$ The integral in rectangular coordinates is ${\displaystyle \underset{-4\sqrt[\phantom{2}]{3}}{\overset{\phantom{}}{}}}{\displaystyle \underset{-\sqrt[\phantom{2}]{48-x^2}}{\overset{}{}}}{\displaystyle \underset{4}{\overset{}{}}}dzdydx.$

$($Type exact answers, using $$ as needed.$)$

$($d$)$ The volume is $$

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