Solve the Problem $D$ Be the Region Bounded Below by The $x y$

question 151

Multiple Choice

Solve the problem.
-Let $D$ be the region bounded below by the $x y$ -plane, above by the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 64$ , and on the sides by the cylinder $x ^ { 2 } + y ^ { 2 } = 36$ . Set up the triple integral in cylindrical coordinates that gives the volume of $D$ using the order of integration $\mathrm { d } \theta \mathrm { dz } \mathrm { dr }$ .

• A) \(\int _ { 0 } ^ { 8 } \int _ { 0 } ^ { \sqrt { 36 - r ^ { 2 } } } \int _ { 0 } ^ { 2 \pi } r d \theta d z d r\)
• B) \(\int _ { 0 } ^ { 6 } \int _ { 0 } ^ { \sqrt { 64 - r ^ { 2 } } } \int _ { 0 } ^ { 2 \pi } r d \theta d z d r\)
• C) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 64 - r ^ { 2 } } } \int _ { 0 } ^ { 8 } r d \theta d z d r\)
• D) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 64 - r ^ { 2 } } } \int _ { 0 } ^ { 6 } r d \theta d z d r\)

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