Solve the Problem $I _ { Z }$ Of the Rectangular Solid of Density

Multiple Choice

Solve the problem.
-Find the moment of inertia $I _ { Z }$ of the rectangular solid of density $\delta ( x , y , z ) = x y z$ defined by $0 \leq x \leq 9,0 \leq y \leq 7$ , $0 \leq \mathrm { z } \leq 3$ .

A) $\frac { 2,321,865 } { 8 }$
B) $\frac { 4,965,219 } { 16 }$
C) $\frac { 1,035,909 } { 8 }$
D) $\frac { 1,607,445 } { 8 }$