Explanation Given information: The height of cone is always two third of the radius and height is 4 inches. Also, volume of salt pile is changing at the rate of 3 cubic/sec. Concept and Formula Used: The following differentiation formula are used: d d x ( x n ) = n x n − 1 , Volume of cone is V = 1 3 π r 2 h Calculation: The Volume of cone is V = 1 3 π r 2 h Also h = 2 3 r Then V = 1 3 π r 2 ( 2 3 r ) V = 2 9 π r 3 Differentiate both sides with respect to ‘t’ d d t V = d d t ( 2 9 π r 3 ) d V d t = 2 9 π d d t r 3 Using d d x ( x n

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Chapter 3.5, Problem 53A

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To Calculate: The rate of change of radius of the conical salt pile.

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Chapter 3.5, Problem 52A

Chapter 3.5, Problem 54A

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Chapter 3 Solutions

Calculus

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The rate of change of radius of the conical salt pile.

Solution Summary: The author explains the rate of change of radius of the conical salt pile.

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To Calculate: The rate of change of radius of the conical salt pile.

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Chapter 3 Solutions