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:

Perpetuity

A type of financial asset that generates a never-ending stream of cash flows or payments with no expiration date.

Equal Payments

Regularly scheduled payments of the same amount, often used in loans and amortization schedules.

Equal Intervals

Equal intervals refer to divisions or measurements in data that have the same length or duration between them, commonly used in statistical analysis and research.

Received

To have taken possession or delivery of an item, payment, or communication.