Find the Volume of the Solid Generated by Revolving the Region

question 6

Multiple Choice

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line. Sketch the region and a representative rectangle.
$y = 16 - x ^ { 2 } , y = 0 ;$ the line $x = - 4$

• A) \(256 \pi\)
• B) \(\frac { 1,024 } { 3 } \pi\)
• C) \(512 \pi\)
• D) \(\frac { 2,048 } { 3 } \pi\)

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Definitions:

Normally Distributed Random Variable

A type of random variable whose values are symmetrically distributed around the mean, forming a bell-shaped curve when graphed.

Mean

The arithmetic average of a set of numbers, calculated by summing all the numbers and then dividing by the count of those numbers.

Standard Deviation

Standard deviation is a measure that quantifies the amount of variation or dispersion of a set of data values from their mean.

Standard Normal Random Variable

A normally distributed random variable characterized by a mean of 0 and a standard deviation of 1.