Explanation Let the area of any sphere with radius r be S = 4 π r 2 We are going to use differentials to estimate the effect of 1% increase in radius on surface area. Differentiating S w.r.t. r, d S = 8 π r d r d r = 1 % ( r ) = r 100 Also, ( 100 % ) d S S = ( 100 % ) 8 π r d r 4 π r 2 Plugging the value of d r , = 8 π r &#

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 3.8, Problem 37PS

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A certain cell is modelled as a sphere. If the formulas S=4πr2 and V=43πr3 are used to compute the surface area and volume of the sphere, respectively, estimate the effect on S and V produced by a 1% increase in the radius r.

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Chapter 3.8, Problem 36PS

Chapter 3.8, Problem 38PS

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Chapter 3 Solutions

Calculus

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A certain cell is modelled as a sphere. If the formulas S = 4 π r 2 and V = 4 3 π r 3 are used to compute the surface area and volume of the sphere, respectively, estimate the effect on S and V produced by a 1% increase in the radius r.

Solution Summary: The author explains how the formulas S and V are used to compute the surface area and volume of the sphere.

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A certain cell is modelled as a sphere. If the formulas S=4πr2 and V=43πr3 are used to compute the surface area and volume of the sphere, respectively, estimate the effect on S and V produced by a 1% increase in the radius r.

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