A Spherical Weather Balloon Is Being Inflated in Such a Way

question 17

Multiple Choice

A spherical weather balloon is being inflated in such a way that the radius is given by $r = g ( t ) = \frac { 1 } { 2 } t + 2$ Assume that r is in meters and t is in seconds, with t = 0 corresponding to the time that inflation begins. If the volume of a sphere of radius r is given by $V ( r ) = \frac { 4 } { 3 } \pi r ^ { 3 }$ find the time at which the volume of the balloon is $36 \pi \mathrm { m } ^ { 3 }$

• A) t = 5 sec
• B) t = 6 sec
• C) t = 3 sec
• D) t = 2 sec
• E) t = 1 sec

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Definitions:

Argument By Anecdote

A method of argument where personal stories or anecdotes are used as evidence, often overlooking statistical or scientific evidence.

Critical Thinking

The intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information.

Oversimplification

The reduction of a complex issue or situation to simplistic terms or concepts, which often leads to misunderstanding or misrepresentation.

Critical Thinking

The objective analysis and evaluation of an issue in order to form a judgment.