Solve the Problem $\mathrm { I } _ { \mathrm { y } }$

Multiple Choice

Solve the problem.
-Find the moment of inertia $\mathrm { I } _ { \mathrm { y } }$ of a tetrahedron of constant density $\delta ( x , y , z ) = x + y + z$ bounded by the coordinate planes and the plane $\frac { x } { 4 } + \frac { y } { 7 } + \frac { z } { 8 } = 1$ .

A) $\frac { 74,816 } { 27 }$
B) $\frac { 74,816 } { 45 }$
C) $\frac { 74,816 } { 47 }$
D) 2338