Find the Volume of the Solid Generated by Revolving the Region

question 11

Multiple Choice

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines.
$y = 22 - 10 x - x ^ { 2 } , y = x + 22$
(i) $x$ -axis; (ii) the line $y = 11$

• A) (i) \(\frac { 117,128 } { 15 } \pi ; \frac { 190,333 } { 15 } \pi\)
• B) (i) \(\frac { 58,564 } { 15 } \pi ; \frac { 190,333 } { 30 } \pi\)
• C) (i) \(\frac { 380,666 } { 15 } \pi ; \frac { 234,256 } { 15 } \pi\)
• D) (i) \(\frac { 190,333 } { 30 } \pi ; \frac { 58,564 } { 15 } \pi\)
• E) (i) \(\frac { 190,333 } { 15 } \pi ; \frac { 117,128 } { 15 } \pi\)

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Definitions:

S Index Fund

A type of mutual fund or exchange-traded fund (ETF) that replicates the performance of a specific benchmark index, often used for passive investing.

PHStat

An Excel add-in program that enhances the statistical analysis capabilities of Microsoft Excel, often used for educational purposes or in decision-making processes.

Standard Deviation

A measure of the amount of variation or dispersion of a set of values, indicating how much the individual values in a dataset deviate from the mean.

Covariance

A measure of the degree to which two variables change together, indicating the direction of their linear relationship.