Solve the Problem By Transforming to Cylindrical or Spherical Coordinates $\frac { 2 \pi } { 3 } \left( 9 - ( 5 ) ^ { 3 / 2 } \right)$

question 44

Multiple Choice

Solve the problem.
-Evaluate
$$\int _ { - 2 } ^ { 2 } \int _ { - \sqrt { 4 - y ^ { 2 } } } ^ { \sqrt { 4 - y ^ { 2 } } } \int _ { 0 } ^ { \sqrt { 9 - x ^ { 2 } - y ^ { 2 } } } d z d x d y$$
by transforming to cylindrical or spherical coordinates.

• A) \(\frac { 2 \pi } { 3 } \left( 9 - ( 5 ) ^ { 3 / 2 } \right)\)
• B) \(\frac { 2 \pi } { 3 } \left( 27 - ( 5 ) ^ { 3 / 2 } \right)\)
• C) \(\frac { 4 \pi } { 3 } \left( 9 - ( 5 ) ^ { 3 / 2 } \right)\)
• D) \(\frac { 4 \pi } { 3 } \left( 27 - ( 5 ) ^ { 3 / 2 } \right)\)

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