Let W Be the Region Between the Spheres $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 1$

question 26

Multiple Choice

Let W be the region between the spheres $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 1$ and $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$ .Given that $\int _ { W } \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) ^ { 1 / 2 } d V = 15 \pi$ , evaluate the integral $\int _ { w } \left( 64 x ^ { 2 } + 36 y ^ { 2 } + 144 z ^ { 2 } \right) ^ { 1 / 2 } d V$ , where $\bar{W}$ is the region between the ellipsoids $\frac { x ^ { 2 } } { 3 ^ { 2 } } + \frac { y ^ { 2 } } { 4 ^ { 2 } } + \frac { z ^ { 2 } } { 2 ^ { 2 } } = 1$ and $\frac { x ^ { 2 } } { 3 ^ { 2 } } + \frac { y ^ { 2 } } { 4 ^ { 2 } } + \frac { z ^ { 2 } } { 2 ^ { 2 } } = 4$ .

• A) \(8640 \pi\)
• B) \(2160 \pi\)
• C) \(24 \pi\)
• D) \(360 \pi\)
• E) \(360 \pi ^ { 3 }\)

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Definitions:

Situational Leadership Model

A leadership theory proposing that effective leadership varies according to, and must adapt to, the needs of the situation and the readiness of the team being led.

Delegating

The act of assigning responsibility and authority to another person to carry out specific activities, while the delegator retains overall responsibility for the outcome.

Hersey-Blanchard Situational Leadership Model

A theory that suggests the most effective leadership style varies according to the task at hand and the maturity level of the team or individual being led.

Vroom-Jago Leader-Participation Model

A decision-making framework for leaders that helps determine the level of involvement of team members in the decision-making process.