Use the Shell Method to Find the Volume of the Solid

question 165

Multiple Choice

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated line.
-About the line $y = 5$


$$x = 5 y - y ^ { 2 }$$

• A) \(\frac { 625 } { 3 } \pi\)
• B) \(\frac { 625 } { 12 } \pi\)
• C) \(\frac { 625 } { 6 } \pi\)
• D) \(\frac { 125 } { 6 } \pi\)

---

Definitions:

Rating Scale

A method for measuring a variable or for categorizing with the intent to represent quantities or qualities with numbers or symbols.

Panic Disorder

A mental health condition that is characterized by sudden and frequent episodes of intense fear accompanied by physical symptoms such as heart palpitations, dizziness, and shortness of breath.

Obsessive-compulsive Disorder

A mental health disorder characterized by repetitive, unwanted thoughts (obsessions) and behaviors (compulsions) that one feels the urge to repeat over and over.

Generalized Anxiety Disorder

Generalized Anxiety Disorder is a mental health condition characterized by persistent and excessive worry about various aspects of daily life, often accompanied by physical symptoms like fatigue, restlessness, or sleep disturbances.