Find the Volume of the Solid Generated by Revolving the Region

question 113

Multiple Choice

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.
- $$y = x ^ { 2 } + 3 , y = 3 x + 3$$

• A) \(27 \pi\)
• B) \(\frac { 297 } { 10 } \pi\)
• C) \(\frac { 513 } { 5 } \pi\)
• D) \(\frac { 297 } { 5 } \pi\)

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Definitions:

Rubrospinal

Referring to the rubrospinal tract, which is a pathway in the central nervous system that helps mediate voluntary motor control.

Vestibulospinal

Relating to the vestibulospinal tract, a pathway in the central nervous system that conveys information from the vestibular system to motor neurons controlling limb and trunk muscles for balance.

Cerebral Cortex

The outer layer of the cerebrum, involved in various high-level brain functions such as thought, memory, and emotion.

Pyramids

In anatomy, this term refers to the pyramidal tracts of the brain, which are major pathways for motor communication from the brain to the spinal cord. Alternatively, it could reference the ancient monumental structures built as tombs for Pharaohs in Egypt.