Find the Volume of the Solid Generated by Revolving the Region

question 30

Multiple Choice

Find the volume of the solid generated by revolving the region about the given line.
-The region bounded above by the line $y = 8$ , below by the curve $y = 8 \cos ( \pi x )$ , on the left by the line $x = - 0.5$ , and on the right by the line $x = 0.5$ , about the line $y = 8$

• A) \(32 \pi\)
• B) \(192 \pi - 128\)
• C) \(96 \pi\)
• D) \(96 \pi - 256\)

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Definitions:

Isocost Line

A graph representing all combinations of inputs that have the same total cost for a firm.

Price of Capital

The cost of borrowing money to purchase or invest in capital assets, often reflected in interest rates or return expectations.

Price of Labor

The compensation received by workers for their services, typically in the form of wages or salaries, which can be influenced by factors such as skill levels, supply and demand, and economic conditions.

Total Expenditure

The aggregate amount of spending by an entity or economy on goods and services, including consumption, investment, government purchases, and net exports.