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

question 43

Multiple Choice

Use spherical coordinates to evaluate $\iiint _ { B } \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } d V$ , where $B$ is the ball $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \leq 7$ .
Select the correct answer.

• A) \(2401 \pi\)
• B) \(343 \pi\)
• C) \(686 \pi\)
• D) \(7 \pi\)

---

Definitions:

Economic Development

The process by which the overall health, well-being, and academic level of a population in a specific area is improved through targeted policies and projects.

Birth Rate

The number of live births per thousand people in a population over a specific period of time.

City Centers

Central areas of cities that often contain a concentration of cultural, commercial, and civic activities.

Total Fertility Rate

The average number of children that would be born to a woman over her lifetime under current age-specific fertility rates.