Evaluate the Triple Integral $\iiint _ { E } \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) d V$

Multiple Choice

Evaluate the triple integral $\iiint _ { E } \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) d V$ in spherical coordinates, where E is the solid in the first octant bounded by the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$ and the coordinate planes.

A) $\frac { 32 \pi } { 5 }$

B) $\frac { 4 \pi } { 5 }$

C) $\frac { \pi } { 2 }$

D) $\frac { 2 \pi } { 3 }$

E) $\frac { 16 \pi } { 5 }$

F) $\pi$

G) $\frac { 4 \pi } { 3 }$

H) 2 $\pi$