Use Spherical Coordinates $\iiint _ { B } \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) ^ { 2 } d V$

Multiple Choice

Use spherical coordinates. Evaluate $\iiint _ { B } \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) ^ { 2 } d V$ , where $B$ is the ball with center the origin and radius $5$ .

A) $\frac { 312500 } { 7 } \pi$
B) $\frac { 4374 } { 7 }$
C) $\frac { 4374 } { 7 } \pi$
D) $\frac { 559872 } { 7 } \pi$
E) None of these