Explanation Given information: Given that a bead is formed by removing a cylinder of radius r from the center of sphere of radius R. The figure is given below Formula used: Using the concept of disk method to determine the volume of the given shaded region which is V = π ∫ [ ( outer radius ) 2 − ( inner radius ) 2 ] d y Calculation: Consider the below figure Here, triangle OAB is right angle triangle so using Pythagorean theorem R 2 = r 2 + ( h 2 ) 2 h 2 = R 2 − r 2 ...... ( 1 ) Now, taking a strip parallel to x axis which goes from x = r to x = R 2 − y 2 . Also, along y axis strip goes from − h / 2 to h / 2 . So, volume of the bead is given by V = π ∫ − h / 2 h / 2 [ ( R 2 − y 2 ) 2 − r 2 ] d y = π ∫ − h / 2 h / 2 [ R 2 − y 2 − r 2 ] d y = π [ ( R 2 − r 2 ) y − y 3 3 ] − h / 2 h / 2 = π [ ( ( R 2 − r 2 ) h 2 −

Loose-leaf Version For Calculus: Early Transcendentals

4th Edition

ISBN: 9781319055912

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Question

Chapter 6.3, Problem 63E

To determine

Tocalculate:

the volume of the bead with given data.

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Chapter 6.3, Problem 62E

Chapter 6.3, Problem 64E

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Chapter 6 Solutions

Loose-leaf Version For Calculus: Early Transcendentals

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Tocalculate: the volume of the bead with given data.

Solution Summary: The author calculates the volume of the bead by removing a cylinder of radius r from the center of sphere.