Find the Volume of the Solid Generated by Revolving the Region

question 56

Multiple Choice

Find the volume of the solid generated by revolving the region about the given line.
-The region in the first quadrant bounded above by the line $y = 2$ , below by the curve $y = \sqrt { 2 x }$ , and on the left by the $y$ -axis, about the line $x = - 1$

• A) \(\frac { 64 } { 15 } \pi\)
• B) \(\frac { 8 } { 5 } \pi\)
• C) \(\frac { 16 } { 5 } \pi\)
• D) \(\frac { 18 } { 5 } \pi\)

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Definitions:

Paranoid Delusions

False beliefs of persecution or conspiracy that are not grounded in reality, often observed in certain psychotic disorders.

Violent Behavior

Actions that involve physical force intended to hurt, damage, or kill someone or something, often stemming from various psychological or social factors.

Major Depressive Disorder

A mental health condition marked by persistent feelings of sadness, loss of interest, and a lack of energy, affecting daily functioning.

Auditory Hallucinations

Experiencing hearing voices or sounds that have no physical source and are not heard by others, often associated with mental health conditions.