If $\sigma ( x , y , z ) = k$

Multiple Choice

If $\sigma ( x , y , z ) = k$ is the volume density of the solid bounded by $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$ then its moment of inertia about the z-axis is

A) $\frac { 512 \pi k } { 75 }$
B) $\frac { 256 \pi k } { 75 }$
C) $\frac { 256 \pi k } { 15 }$
D) $\frac { 512 \pi k } { 15 }$
E) $\frac { 128 \pi k } { 15 }$