The Disk $( x - 4 ) ^ { 2 } + y ^ { 2 } \leq 1$

question 36

Multiple Choice

The disk $( x - 4 ) ^ { 2 } + y ^ { 2 } \leq 1$ is revolved about the $y$ -axis to generate a torus. Find its volume. (Hint: $\int _ { - 1 } ^ { 1 } \sqrt { 1 - y ^ { 2 } } d y = \frac { 1 } { 2 } \pi$ , since it is the area of a semicircle of radius 1 .)

• A) \(8 \pi ^ { 2 }\)
• B) \(2 \pi ^ { 2 }\)
• C) \(4 \pi ^ { 2 }\)
• D) \(4 \pi\)

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Definitions:

Increasing Cost Industry

An industry where production costs increase as output expands, typically due to factors like resource depletion or increased expenses for inputs.

Long Run

The long run is a period in economic theory during which all factors of production and costs are variable, allowing firms to adjust all inputs to attain desired output levels.

Per-unit Costs

The cost incurred for producing a single unit of product, often calculated to analyze efficiency or profitability.

Increasing Cost Industry

An industry where production costs rise as output increases due to factors such as limited resources or higher wages.