Solve the Problem $\mathrm { V }$ (In Cubic Inches) of a Cylindrical Pipe with Length 12

question 38

Essay

Solve the problem.
-The volume $\mathrm { V }$ (in cubic inches) of a cylindrical pipe with length 12 inches is given by $\mathrm { V } ( \mathrm { r } ) = 12 \pi \mathrm { r } ^ { 2 }$ , where $r$ is the radius of the piston (in inches). If the radius is increasing with time $t$ (in minutes) according to the formula $r ( t ) = \frac { 1 } { 6 } t ^ { 2 } , t \geq 0$ , find the volume $V$ of the pipe as a function of the time $t$

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Definitions:

Personal Optimism

An individual's tendency to hold a positive outlook towards their future or the outcome of specific endeavors.

Coping With Stress

Various strategies and methods used by individuals to handle, reduce, or manage their stress and its effects on their lives.

Optimism And Pessimism

Psychological tendencies to generally expect positive or negative outcomes, respectively, which can impact behavior and mental health.

Problem-Focused Coping

A coping strategy aimed at addressing or changing the root cause of a stressor rather than simply alleviating its symptoms.