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

Multiple Choice

Solve the problem.
-Find the moment of inertia $\mathrm { I } _ { \mathrm { y } }$ of the region of constant density $\delta ( x , y , z ) = 1$ bounded by the paraboloid $z = 64 - x ^ { 2 } - y ^ { 2 }$ and the $x y$ -plane.

A) $\frac { 4,259,840 } { 3 } \pi$
B) $\frac { 17,039,360 } { 9 } \pi$
C) $\frac { 532,480 } { 3 } \pi$
D) $\frac { 66,560 } { 3 } \pi$