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

question 114

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\(\pi\)

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