Set Up a Triple Integral That Gives the Moment of Inertia

Multiple Choice

Set up a triple integral that gives the moment of inertia about the $z \text {-axis of the solid }$ region $Q$ of density given below.
$\begin{array} { l } \rho ( x , y , z ) = \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } \\Q = \{ - 4 \leq x \leq 4 , - 4 \leq y \leq 4,0 \leq z \leq 1 - y \}\end{array}$

A)
$\int_{-4}^{4}\int_{-4}^{4}\int_{0}^{1-x}\left(x^{2}+y^{2}\right) \sqrt{x^{2}+y^{2}+z^{2}} d z d y d x$

B)
$\int_{-4}^{4}\int_{-4}^{4}\int_{0}^{1-x}\left(x^{2}+y^{2}\right) \sqrt{x^{2}+y^{2}+z^{2}} d y d z d x$
C)
$\int_{-4}^{4}\int_{-4}^{4}\int_{0}^{1-y}\left(x^{2}+y^{2}\right) \sqrt{x^{2}+y^{2}+z^{2}} d z d y d x$

D)
$\int_{-4}^{4}\int_{-4}^{4}\int_{0}^{1-x}\left(x^{2}+z^{2}\right) \sqrt{x^{2}+y^{2}+z^{2}} d z d y d x$

E)
$\int_{-4}^{4}\int_{-4}^{4}\int_{0}^{1-y}\left(z^{2}+y^{2}\right) \sqrt{x^{2}+y^{2}+z^{2}} d z d y d x$