Suppose That $f ( x , y , z ) = g \left( \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } \right)$

question 68

Multiple Choice

Suppose that $f ( x , y , z ) = g \left( \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } \right)$ where g is a function of one variable such that $g ( 5 ) = 8$ . Evaluate $\iint _ { S } f ( x , y , z ) d S$ where S is the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 25$

• A) \(920 \pi\)
• B) \(820 \pi\)
• C) \(800 \pi\)
• D) \(880 \pi\)
• E) None of these

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Definitions:

Compound

Substance having two or more different elements in a fixed ratio.

Molecules

Groups of two or more atoms held together by chemical bonds.

Nucleus

A membrane-bound organelle found in eukaryotic cells that contains most of the cell's genetic material.

Neutrons

Neutral, subatomic particles found in the nucleus of an atom, contributing to the atom's mass but not its charge.