Evaluate $\iiint _ { T } f ( x , y , z ) d V$

question 57

Multiple Choice

Evaluate $\iiint _ { T } f ( x , y , z ) d V$ where $f ( x , y , z ) = 7 y$ and T is the region bounded by the paraboloid $y = x ^ { 2 } + z ^ { 2 }$ and the plane $y = 1$

• A) \(\frac { 7 } { 3 }\) \(\pi\)
• B) \(\frac { 1 } { 7 }\) \(\pi\)
• C) \(\frac { 49 } { 3 }\) \(\pi\)
• D) \(7\) \(\pi\)

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Definitions:

Ethical Dilemma

A situation where an individual faces a choice between two morally right or conflicting principles where choosing one means compromising the other.

Ethical Absolutism

The belief in universal ethical standards that apply to all cultures and individuals regardless of context or situation.

Situational Ethics

A philosophy that ethical decisions should be made based on the context of a particular situation rather than by following absolute moral rules.

Deontology

A branch of ethics that focuses on the morality of actions based on adherence to defined rules or duties, regardless of the outcomes.