Evaluate the Triple Integral $\iiint _ { E } \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } d V$

Multiple Choice

Evaluate the triple integral $\iiint _ { E } \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } d V$ in spherical coordinates, where E is the solid bounded by the hemisphere $z = \sqrt { 4 - x ^ { 2 } - y ^ { 2 } }$ and the plane z = 0.

A) $\frac { \pi } { 4 }$

B) 16 $\pi$

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

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

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

F) 8 $\pi$

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

H) 2 $\pi$