Find the Volume of the Indicated Region $x ^ { 2 } + y ^ { 2 } = 100$

question 18

Multiple Choice

Find the volume of the indicated region.
-the region common to the interiors of the cylinders $x ^ { 2 } + y ^ { 2 } = 100$ and $x ^ { 2 } + z ^ { 2 } = 100$

• A) \(\frac { 4000 } { 3 }\)
• B) 4000
• C) \(\frac { 16000 } { 3 }\)
• D) \(\frac { 2000 } { 3 }\)

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Definitions:

Central

Pertaining to the center or most important part of an object, area, or function.

Peripheral

Relating to or situated on the edge or periphery of something; in medical terms, it often refers to the outer regions of the body, such as the limbs.

Autonomic

Relating to the autonomic nervous system, which controls involuntary bodily functions such as heart rate, digestion, and respiratory rate.

Vertigo

A sensation of spinning or dizziness, often related to problems in the inner ear.