Find the Area of the Part of the Sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 16$

question 55

Multiple Choice

Find the area of the part of the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 16$ above the plane z = 2.

• A)3\(\pi\)
• B)2\(\pi\)
• C)4\(\pi\)
• D)8\(\pi\)
• E)12\(\pi\)
• F)6\(\pi\)
• G)16\(\pi\)
• H)8

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Definitions:

Budget Line

A line that represents all combinations of goods and services a consumer can purchase with their income at given prices.

Marginal Rate

Generally refers to the rate at which one quantity changes with respect to a change in another, often used in the context of taxes or substitution rates.

Indifference Curve

A visual depiction illustrating various pairings of two products that deliver the same degree of happiness and usefulness to a buyer.

Substitution

The act of replacing one item or factor with another due to factors like cost, preferences, or availability, often affecting consumer choices and market dynamics.