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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Definitions:

Total Product Curve

A graphical representation that shows the relationship between the total output produced by a firm and the quantity of input used, illustrating the production function.

Interest-Rate Cost-Of-Funds

The expense associated with borrowing money, typically expressed as a percentage rate, impacting the cost of accessing funds for lending or investment.

Expected Rate of Return

The anticipated earnings on an investment, typically expressed as an annual percentage.

Marginal Utility

The change in satisfaction or utility an individual gains from consuming an additional unit of a good or service.