A ruptured pipe in an offshore oil rig produces a circular oil slick that is T feet

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A ruptured pipe in an offshore oil rig produces a circular oil slick that is T feet thick at a distance r feet from the rupture, where


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At the time the spill is contained, the radius of the slick is 7 feet. We wish to find the volume of oil that has been spilled.


a. Sketch the graph of T(r). Notice that the volume we want is obtained by rotating the curve T(r) about the T axis (vertical axis) rather than the r axis (horizontal axis).


b. Solve the equation


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for r in terms of T. Sketch the graph of r(T), with T on the horizontal axis.


c. Find the required volume by rotating the graph of r(T ) found in part (b) about the T axis.

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Calculus For Business, Economics And The Social And Life Sciences

ISBN: 9780073532387

11th Brief Edition

Authors: Laurence Hoffmann, Gerald Bradley, David Sobecki, Michael Price

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