Use the Shell Method to Find the Volume of the Solid

question 169

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 x-axis.
- $$y = \sqrt { x } , y = 0 , y = x - 6$$

• A) \(27 \pi\)
• B) \(\frac { 63 } { 4 } \pi\)
• C) \(\frac { 225 } { 2 } \pi\)
• D) \(\frac { 63 } { 2 } \pi\)

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Definitions:

Yates' Correction

A statistical adjustment made to the chi-squared test for small sample sizes, to better approximate the chi-squared distribution.

Expected Frequencies

The predicted counts of occurrences across different categories or intervals that one would expect by chance.

Fisher's Exact Test

A statistical significance test used to determine if there are nonrandom associations between two categorical variables, often employed when sample sizes are small.

Yates' Correction

A continuity correction method used in Chi-square tests to adjust for the discontinuity of a chi-square distribution when working with discrete variables.