Use the Shell Method to Find the Volume of the Solid

question 29

Multiple Choice

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


$y = 3 x - x ^ { 2 }$

• A) \(\frac { 27 } { 4 } \pi\)
• B) \(\frac { 81 } { 4 } \pi\)
• C) \(\frac { 27 } { 2 } \pi\)
• D) \(\frac { 81 } { 8 } \pi\)

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Definitions:

Noon

The middle of the day, typically regarded as 12:00 PM, when the Sun is at its highest point in the sky.

Carbon Dioxide

A colorless, odorless gas produced by burning carbon and organic compounds and by respiration. It is naturally present in air and absorbed by plants in photosynthesis.

Photosynthesis

The process by which green plants and some other organisms use sunlight to synthesize foods with carbon dioxide and water.

Internal Concentration

The concentration of substances within a cell or organism in contrast to the external environment, crucial for maintaining homeostasis.