Use the Shell Method to Find the Volume of the Solid

question 71

Multiple Choice

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis.
- $$y = \frac { 6 } { x } , y = 0 , x = 7 , x = 9$$

• A) \(36 \pi\)
• B) \(24 \pi\)
• C) \(18 \pi\)
• D) \(12 \pi\)

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Definitions:

Sigma Complex

An intermediate in certain chemical reactions characterized by a covalent bond (sigma bond) between the reactant and a metal atom from the catalyst.

Nitroacetophenone

An organic compound containing both a nitro group and an acetyl group attached to a benzene ring, used in the synthesis of dyes and pharmaceuticals.

Bromination

A chemical reaction involving the addition of bromine (Br2) to organic compounds, typically to add bromine atoms or convert double bonds into Br-containing derivatives.

Bromobenzene

An aromatic bromine compound used frequently in organic synthesis, as a bromination precursor for making various organic products.