Use Spherical Coordinates to Evaluate $\iiint _ { B } \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } d V$

question 16

Multiple Choice

Use spherical coordinates to evaluate $\iiint _ { B } \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } d V$ , where $B$ is the ball $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \leq 10$ .

• A) \(10000 \pi\)
• B) \(10 \pi\)
• C) \(1000 \pi\)
• D) \(2000 \pi\)

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Definitions:

3-Methylbutanoic Acid

An organic compound with the formula C5H10O2, known for its pungent odor resembling sweat or body odor.

Synthesis

The process of combining two or more entities to form something new; in chemistry, it refers to the creation of complex chemical compounds from simpler ones.

Predominant Form

The most abundant or stable form of a chemical species under specified conditions.

L-Valine

An essential amino acid used in the biosynthesis of proteins, with a particular importance in muscle metabolism and tissue repair.