Use the Shell Method to Find the Volume of the Solid

question 134

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 $y = 5$


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

• A) \(\frac { 63 } { 2 } \pi\)
• B) \(\frac { 63 } { 4 } \pi\)
• C) \(\frac { 27 } { 2 } \pi\)
• D) \(\frac { 189 } { 2 } \pi\)

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Definitions:

FMV

Fair Market Value, an estimation of the market value of a property or asset, based on what a knowledgeable, willing, and unpressured buyer would likely pay to a knowledgeable, willing, and unpressured seller in the market.

Adjusted Basis

The original cost of an asset adjusted for factors such as depreciation or improvements, used to calculate capital gains or losses for tax purposes.

Straight-line Depreciation

A method of calculating the depreciation of an asset evenly over its useful life.

Single Category Average Cost Method

A method for calculating the cost basis of mutual funds, ETFs, or stocks for tax purposes, where all shares are considered to have the same average cost.