Find the Area of the Part of the Hemisphere $z = \sqrt { 4 - x ^ { 2 } - y ^ { 2 } }$

question 212

Multiple Choice

Find the area of the part of the hemisphere $z = \sqrt { 4 - x ^ { 2 } - y ^ { 2 } }$ that lies above the area inside the circle $x ^ { 2 } + y ^ { 2 } = 1$ .

• A) \(( 4 - 2 \sqrt { 2 } ) \pi\)
• B) \(( 6 - 3 \sqrt { 2 } ) \pi\)
• C) \(( 8 - 4 \sqrt { 2 } ) \pi\)
• D) \(( 6 - 3 \sqrt { 3 } ) \pi\)
• E) \(( 8 - 4 \sqrt { 3 } ) \pi\)
• F)6\(\pi\)
• G)8\(\pi\)
• H)16\(\pi\)

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Definitions:

Marginal Utility

The boost in happiness or utility a consumer gets from buying one more unit of a product or service.

Utility Maximization

The economic principle that individuals seek to obtain the highest level of satisfaction or utility from their consumption choices, given their preferences and constraints.

Hypothetical Consumer

A model or theoretical individual used in economics and marketing to represent and analyze consumer behavior and decision-making processes.

Utility Maximization

The economic principle that individuals or firms attempt to allocate their resources in a manner that maximizes their satisfaction or profit.