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 −

4th Edition

ISBN: 9781319379421

Author: Rogawski

Publisher: MAC HIGHER

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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

Chapter 6 Solutions

CALCULUS 4E (HC) W/ ACHIEVE ACCESS

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Prob. 32E Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Prob. 37E Ch. 6.1 - Prob. 38E Ch. 6.1 - Prob. 39E Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Prob. 42E Ch. 6.1 - Prob. 43E Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Prob. 48E Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.1 - Prob. 51E Ch. 6.1 - Prob. 52E Ch. 6.1 - Prob. 53E Ch. 6.1 - Prob. 54E Ch. 6.1 - 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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.