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

question 19

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 $\rho = 4$ . Set up the triple integral for the volume of $D$ in spherical coordinates.

• A) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \pi / 2 } \int _ { 0 } ^ { 4 }\) Q\(^ { 2 } \sin \varphi \operatorname { de } d \varphi d \theta\)
• B) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \pi / 4 } \int _ { 0 } ^ { 4 } \rho ^ { 2 } \sin \varphi \mathrm { de } \mathrm { d } \varphi \mathrm { d } \theta\)
• C) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 3 \pi / 4 } \int _ { 0 } ^ { 4 } \rho ^ { 2 } \sin \varphi \operatorname { de } d \varphi \mathrm { d } \theta\)
• D) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \pi } \int _ { 0 } ^ { 4 } \rho ^ { 2 } \sin \varphi \mathrm { de } \mathrm { d } \varphi \mathrm { d } \theta\)

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