This exercise is adapted from a problem from the textbook. The image is taken from the textbook as well. Consider "the solid between the sphere p = cos() and the hemisphere p = 2, z ≥ 0" (p. 951). p = cos d = 2 4 1. Recall that the volume of a sphere is ³. Using basic geometry, find the volume of this solid by considering this solid carefully. Notice that this shape is a little complicated. Explain your reasoning. 2. Express the volume of the solid as a triple integral in spherical coordinates. 3. Evaluate the integral you obtained in #2. Confirm that the answer you obtained matches the value you found in #1.
This exercise is adapted from a problem from the textbook. The image is taken from the textbook as well. Consider "the solid between the sphere p = cos() and the hemisphere p = 2, z ≥ 0" (p. 951). p = cos d = 2 4 1. Recall that the volume of a sphere is ³. Using basic geometry, find the volume of this solid by considering this solid carefully. Notice that this shape is a little complicated. Explain your reasoning. 2. Express the volume of the solid as a triple integral in spherical coordinates. 3. Evaluate the integral you obtained in #2. Confirm that the answer you obtained matches the value you found in #1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Transcribed Image Text:This exercise is adapted from a problem from the textbook. The image is taken from the
textbook as well.
Consider "the solid between the sphere p = cos(p) and the hemisphere p = 2, z ≥ 0" (p.
951).
p = cos d
2
p=2
1. Recall that the volume of a sphere is ³. Using basic geometry, find the volume of
this solid by considering this solid carefully.
Explain your reasoning.
Notice that this shape is a little complicated.
2. Express the volume of the solid as a triple integral in spherical coordinates.
3. Evaluate the integral you obtained in #2. Confirm that the answer you obtained matches
the value you found in #1.
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