Find the Volume of the Solid Obtained When the Region $y = x ^ { 2 } + 1 , y = 1 , \text { and } x = 1$

question 10

Multiple Choice

Find the volume of the solid obtained when the region bounded by the curves $y = x ^ { 2 } + 1 , y = 1 , \text { and } x = 1$ is rotated about the line x =1.

• A) \(\frac { \pi } { 12 }\)
• B) \(8 \pi\)
• C) \(\frac { \pi } { 2 }\)
• D) \(\frac { \pi } { 4 }\)
• E) \(\frac { \pi } { 3 }\)
• F) \(\frac { \pi } { 6 }\)
• G) \(4 \pi\)
• H) \(\frac { 10 \pi } { 3 }\)

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Definitions:

Average Operating Assets

An efficiency metric calculated by averaging the value of a company's operational assets over a period, often used in rate of return calculations.

Direct Material Measures

Quantitative assessments used to determine the amount of direct materials required for production.

Financial Measures

Quantitative metrics used to assess a company's financial health and performance, such as income, cash flow, and profitability ratios.

Internal Business Process Measures

Metrics used to evaluate the efficiency and effectiveness of a company's internal operations.