In a Recent Archaeological Expedition, a Scroll Was Discovered Containing $y=-100 \ln \left(\frac{x}{6}\right)$

question 70

Essay

In a recent archaeological expedition, a scroll was discovered containing a description of a plan to build what appears to be the Tower of Babel.According to the manuscript, the tower was supposed to have a circular cross section and "go up to the heavens" (i.e., be infinitely high).A mathematician was consulted to solve some of the questions posed by the archaeologists.The mathematicians plotted half of the silhouette of the tower on a set of coordinate axes with the y-axis running through the center and discovered that it was approximated by the curve $y=-100 \ln \left(\frac{x}{6}\right)$ .Would such a tower have finite volume? If so, calculate it to the nearest whole number.If not, enter "infinite".

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Definitions:

Reflexive Smiling

An involuntary smile, often occurring in infants, that does not necessarily express happiness or response to social interactions.

Social

Relating to society or its organization; includes social interactions, structure, and function within human groups.

Internal-Based

Predominantly influenced or determined by internal factors or processes.

Reflexive Smile

A smile that does not occur in response to external stimuli. It happens during the month after birth, usually during sleep.