Use the Method of Cylindrical Shells to Find the Volume $y = \sqrt { 16 - x ^ { 2 } } , y = - x + 4 ;$

question 50

Multiple Choice

Use the method of cylindrical shells to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis. Sketch the region and a representative rectangle.
$y = \sqrt { 16 - x ^ { 2 } } , y = - x + 4 ;$ the $y$ -axis

• A) \(\frac { 64 } { 3 } \pi\)
• B) \(\quad 128 \pi\)
• C) \(\frac { 64 } { 3 } \pi\)
• D) \(128 \pi\)

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Definitions:

Exhaustion

A state of extreme physical or mental fatigue, often resulting from stress or extended periods of exertion.

Alarm Reaction

The initial phase in the body's response to stress, mobilizing resources to face the threat or challenge.

Tend-And-Befriend

A behavior exhibited by some animals, including humans, as a stress response, where individuals seek social affiliation and nurturing activities to reduce stress.

General Adaptation Syndrome

A three-phase response (alarm, resistance, exhaustion) of the body to stress, identified by Hans Selye.