(a)
The volume of the solid remains after a round hole was drilled.
(a)
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)
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
CALCULUS:GRAPHICAL,...,AP ED.-W/ACCESS
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