Explanation Given information: Radius ‘r’, Volume ‘V’ and Surface area ‘S’ of Sphereare function of time. Concept and Formula Used: The following differentiation formula are used: d d x ( x n ) = n x n − 1 ,Volume of sphere is V = 4 3 π r 3 , Surface area of sphere S = 4 π r 2 . Calculation: The Volume of Sphere is V = 4 3 π r 3 Differentiate both sides with respect to ‘t’ d d t ( V ) = d d t ( 4 3 π r 3 ) d V d t = 4 3 π d d t r 3 Using d d x ( x n ) = n x n − 1 and chain rule d V d t = 4 3 π ( 3 r 2 ) d r d t d V d t = 4 π r 2 d r d t d r d t = 1 4 π r 2 d V d t ..................

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 3.5, Problem 14C

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Chapter 3 Solutions

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The relation between d V d t and d S d t .

Solution Summary: The author explains the relation between dVt and (). Radius ‘r’, Volume ‘V’ and Surface area ‘S’ of Sphere are function of time.

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