Solve the Problem $\mathrm { D }$ Be the Region That Is Bounded Below by the Cone

question 428

Multiple Choice

Solve the problem.
-Let $\mathrm { D }$ be the region that is bounded below by the cone $\varphi = \frac { \pi } { 4 }$ and above by the sphere $\varrho = 6$ . Set up the triple integral for the volume of $\mathrm { D }$ in cylindrical coordinates.

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

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