Find the Volume of the Solid Generated by Revolving the Region

question 125

Multiple Choice

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.
- $$y = x ^ { 2 } + 5 , y = 3 x + 5$$

• A) \(\frac { 279 } { 10 } \pi\)
• B) \(27 \pi\)
• C) \(\frac { 387 } { 5 } \pi\)
• D) \(\frac { 693 } { 5 } \pi\)

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Definitions:

Contribution Margin

The difference between sales revenue and variable costs, showing how much sales contribute to covering fixed costs and generating profit.

Variable Costs

Expenses that fluctuate with changes in production volume or service levels, such as materials and labor costs.

Fixed Costs

Payments for rent, salaries to employees, and insurance coverages that stay the same, no matter the production or sales figures.

Break-Even Point

The point at which total costs and total revenue are equal, resulting in no net loss or gain.