Calculate the Area of the Surface S $S$ Is the Portion of the Sphere

question 131

Multiple Choice

Calculate the area of the surface S.
- $S$ is the portion of the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 100$ between $z = - 5 \sqrt { 2 }$ and $z = 5 \sqrt { 2 }$ .

• A) \(200 \pi\)
• B) \(10 \sqrt { 2 } \pi\)
• C) \(100 \sqrt { 2 } \pi\)
• D) \(200 \sqrt { 2 } \pi\)

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Definitions:

Acceptable Assumptions

The premises that are considered reasonable and are accepted without requiring empirical evidence, often used as a foundational basis in arguments or theories.

Random Sampling

A method of selecting a sample from a population in such a way that each individual has an equal probability of being chosen, ensuring the representativeness of the sample.

Equal Chance

The principle that in a certain process, event, or situation, all outcomes or participants have the same probability or likelihood of occurring or being selected.

Correlation

A statistical measure that expresses the extent to which two variables change together; if the correlation is positive, as one variable increases, the other does as well.