Solve the Problem $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 16$

question 224

Multiple Choice

Solve the problem.
-Find the mass of the solid in the first octant between the spheres $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 16$ and $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 100$ if the density at any point is inversely proportional to its distance from the origin.

• A) \(28 \mathrm { k } \pi\)
• B) \(168 \mathrm { k } \pi\)
• C) \(14 \mathrm { k } \pi\)
• D) \(21 \mathrm { k } \pi\)

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Definitions:

Colonists

Individuals or groups who settle in a new territory but remain subjects or citizens of their country of origin, often involved in the historical context of expansion and empire-building.

Continent

One of the very large landmasses on the earth's surface, typically separated by oceans.

Land Ethics

A philosophy that stresses the interdependence between humans and the land, promoting the responsible use and conservation of natural resources.

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