Find the Volume of the Solid Generated by Revolving the Region

question 26

Multiple Choice

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.
- $$y = 3 \cos \pi x , y = 0 , x = - 0.5 , x = 0.5$$

• A) \(\frac { 9 } { 2 } \pi\)
• B) \(18 \pi\)
• C) \(9 \pi\)
• D) \(3 \pi\)

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Definitions:

Behavioral Synchrony

The phenomenon where individuals in a group mirror each other's actions or emotions, often leading to increased cohesion and empathy.

Collective Cohesion

The sense of solidarity, unity, and commitment among members of a group, which strengthens their willingness to work together towards common goals.

Belongingness

The human emotional need to be an accepted member of a group, whether it is friends, family, or a larger community.

Emotional Cohesion

The bonding of group members through shared feelings, empathy, or emotional experiences that enhance a sense of unity or togetherness.