A Spherical Balloon with Radius $r$ Inches Has Volume $4 \frac{\pi r^{3}}{3}$

question 77

Short Answer

A spherical balloon with radius $r$ inches has volume $4 \frac{\pi r^{3}}{3}$ .
Find a function that represents the amount of air required to inflate the balloon from a radius of $4 \frac{\pi r^{3}}{3}$ inches to a radius of $r+3$ inches.

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Definitions:

Humanistic Theory

Humanistic theory emphasizes individual potential, self-growth, and the importance of meeting psychological needs for love, esteem, and self-actualization.

Positive Regard

The acceptance, respect, and appreciation that one person shows another, considered essential in humanistic psychology for healthy personal development.

Psychodynamic Theorists

Researchers and clinicians who explore how unconscious processes and childhood experiences affect personality and behavior.

Unconscious Determinants

Factors that influence behavior and decisions without the individual's conscious awareness, rooted in the unconscious mind.