Find the Volume of the Solid Generated by Revolving the Region

question 158

Multiple Choice

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.
- $$y = 3 \csc x , y = 3 \sqrt { 2 } , \frac { \pi } { 4 } \leq x \leq \frac { 3 \pi } { 4 }$$

• A) \(\pi ^ { 2 } + 6 \pi\)
• B) \(9 \pi ^ { 2 } - 18 \pi\)
• C) \(9 \pi ^ { 2 } + 18 \pi\)
• D) \(3 \pi ^ { 2 } - 9 \pi\)

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Definitions:

MC Curve

A graphical representation of how the cost to produce one additional unit (marginal cost) changes as production increases.

AVC Curve

The Average Variable Cost curve, which shows the variable cost per unit at different levels of output.

Loss

A financial situation where expenses exceed revenues, or when an investment's value decreases compared to its purchase price.

Price

The monetary value assigned to a product or service, determined by various factors including supply, demand, and production costs.