If $\sigma ( x , y , z ) = \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } }$

Multiple Choice

If $\sigma ( x , y , z ) = \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } }$ is the volume density of the solid between two concentric spheres with radii 1 and 2, then its moment of inertia about a diameter is

A) $16 \pi$
B) $18 \pi$
C) $24 \pi$
D) $28 \pi$
E) 32 $\pi$