(a)
The volume of the solid remains after a round hole was drilled.
(a)
![Check Mark](/static/check-mark.png)
Answer to Problem 59E
The volume of the solid remain is
Explanation of Solution
Given:
A round hole is drilled in spherical solid having radius r and the hole has a height of
Calculation:
The volume can be find out as:
Let us take volume element in cylindrical coordinates:
Limits can be defined as:
In the above formula, R is the radius of original sphere and
Now, integrate the upper half of the solid and multiply it by
Conclusion:
The volume of the solid remain is
(b)
The unusual about the volume determined.
(b)
![Check Mark](/static/check-mark.png)
Answer to Problem 59E
The unusual about volume determined is that it is independent of radius.
Explanation of Solution
Given:
The volume of the solid remain is
Calculation:
In the volume determined, there is no radius involved. Only height is present in the volume.
This is the unusual fact about the determined volume.
Conclusion:
The unusual about volume determined is that it is independent of radius.
Chapter 7 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning
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