Find the Average Value of F(x, Y, Z) Over the Given

question 166

Multiple Choice

Find the average value of F(x, y, z) over the given region.
- $F ( x , y , z ) = x ^ { 2 } + y ^ { 2 } + z ^ { 2 }$ over the rectangular solid in the first octant bounded by the coordinate planes and the planes $x = 9 , y = 6 , z = 7$

• A) 88
• B) \(\frac { 166 } { 3 }\)
• C) \(\frac { 238 } { 3 }\)
• D) \(\frac { 328 } { 3 }\)

---

Definitions:

Neuron

A neuron is a specialized cell transmitting nerve impulses; a nerve cell, the fundamental unit of the nervous system responsible for receiving and sending electrical signals throughout the body.

Cerebral Spinal Fluid

A clear, colorless body fluid found in the brain and spinal cord, which acts as a cushion for the brain's cortex, providing basic mechanical and immunological protection to the brain inside the skull.

Glial Cells

Non-neuronal cells in the central and peripheral nervous systems that support and protect neurons, playing crucial roles in brain function.

Cushioning Effect

A psychological or physical phenomenon where a buffer exists or is created to lessen the impact of a stressful or negative event.