Solve the Problem $\mathrm { D }$ Be the Region Bounded Below by The

question 284

Multiple Choice

Solve the problem.
-Let $\mathrm { D }$ be the region bounded below by the $x y$ -plane, above by the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 100$ , and on the sides by the cylinder $x ^ { 2 } + y ^ { 2 } = 9$ . Set up the triple integral in cylindrical coordinates that gives the volume of $D$ using the order of integration $\mathrm { dz } \mathrm {} \mathrm { d } \theta \mathrm { dr }$ .

• A) \(\int _ { 0 } ^ { 10 } \int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 9 - r ^ { 2 } } } r d z d \theta d r\)
• B) \(\int _ { 0 } ^ { 10 } \int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 9 - r ^ { 2 } } } d z d \theta d r\)
• C) \(\int _ { 0 } ^ { 3 } \int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 100 - r ^ { 2 } } } r d z d \theta d r\)
• D) \(\int _ { 0 } ^ { 3 } \int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 100 - r ^ { 2 } } } d z d \theta d r\)

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