Explanation Given information: A spherical balloon with radius r inches has volume V ( r ) = 4 3 π r 3 . Calculation: Replacing r in the formula 4 3 π r 3 by r + 1, we get the volume of the sphere with radius r + 1. Here is the situation: The volume of the sphere of radius r : V 1 = 4 3 π r 3 The volume of the sphere of radius r + 1: V 2 = 4 3 π ( r + 1 ) 3 The amount of air required to inflate the balloon from volume V 1 to V 2 is the difference of these two volumes, i.e. V 2 − V 1 = 4 3 π ( r + 1 ) 3 − 4 3 π r 3 = 4 3 π ( ( r + 1 ) 3 − r 3 ) Factoring out by 4 3 π Let’s simplify ( r + 1 ) 3 first: ( r + 1 ) 3 = ( r + 1 ) ⋅ ( r + 1 ) Ȭ

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Question

Chapter 1.1, Problem 28E

To determine

To Find:a function that shows the amount of air required to inflate the balloon from a radius of r inches to a radius r + 1 inches.

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Chapter 1.1, Problem 27E

Chapter 1.1, Problem 29E

Chapter 1 Solutions

Biocalculus

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