Explanation Given : A sphere of radius a from which a central cylinder of radius b has been removed where 0 < b < a Proof : Suppose the radius of the sphere is R and the height of the cylinder is h. Then the radius of the cylinder is R 2 − ( h 2 ) 2 The radius of the horizontal cross-section of the sphere at height y above the diameter is R 2 − y 2 The cross section of the band with the plane at height y is the region inside the larger circle of radius given by R 2 − y 2 and outside the smaller circle of radius given by R 2 − ( h 2 ) 2 The cross section's area is therefore the area of the larger circle - area of the smaller circle. = π ( R 2 − y 2 ) 2 − π ( R 2 − ( h 2 ) 2 ) 2 = π ( ( h 2 ) 2 − y 2 ) The last quantity does not depend on R...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16.4, Problem 41E

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To prove: The volume of a sphere of radius a from which a central cylinder of radius b has been removed where 0 < b < a, only depends on the height of the band that results.

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Chapter 16.4, Problem 40E

Chapter 16.4, Problem 42E

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Chapter 16 Solutions

CALCULUS (CLOTH)

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 5PQ Ch. 16.1 - Prob. 6PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E

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To prove : The volume of a sphere of radius a from which a central cylinder of radius b has been removed where 0 < b < a, only depends on the height of the band that results.

Solution Summary: The author explains that the volume of the sphere of radius a from which the central cylinder of b has been removed only depends on the height of its band.

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To prove: The volume of a sphere of radius a from which a central cylinder of radius b has been removed where 0 < b < a, only depends on the height of the band that results.

Want to see the full answer?

Chapter 16 Solutions

To prove : The volume of a sphere of radius a from which a central cylinder of radius b has been removed where 0 &lt; b &lt; a, only depends on the height of the band that results.

Solution Summary: The author explains that the volume of the sphere of radius a from which the central cylinder of b has been removed only depends on the height of its band.

Videos

To prove: The volume of a sphere of radius a from which a central cylinder of radius b has been removed where 0 < b < a, only depends on the height of the band that results.

Want to see the full answer?

Chapter 16 Solutions

To prove : The volume of a sphere of radius a from which a central cylinder of radius b has been removed where 0 < b < a, only depends on the height of the band that results.