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:

Photoreceptors

Specialized cells found in the retina of the eye that are sensitive to light, converting light signals into neural signals for visual recognition.

Nociceptors

Pain receptors that are sensory neurons found throughout the body, responsible for detecting harmful stimuli and sending pain signals to the brain.

Referred Pain

A pain perceived at a location other than the site of the painful stimulus.

Proprioception

The sense of the relative position of one's own body parts and strength of effort being employed in movement, often referred to as the "sixth sense."