Use the Shell Method to Find the Volume of the Solid

question 111

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

• A) \(\frac { 27 } { 4 } \pi\)
• B) \(\frac { 27 } { 2 } \pi\)
• C) \(9 \pi\)
• D) \(18 \pi\)

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Definitions:

Type I Error

The mistake of rejecting the null hypothesis when it is actually true, commonly referred to as a "false positive" result.

Alpha (α)

A pre-specified significance level in hypothesis testing, representing the probability of making a Type I error, or falsely rejecting the null hypothesis.

Hypothesis Test

A statistical method used to determine if there is enough evidence in a sample of data to infer that a certain condition holds true for the entire population.

Reject

In statistical analysis, to refuse the null hypothesis based on the evidence provided by the test statistic.