4. Let S be the solid that lies above the cone z = /r² + y² and below the sphere r² + y² + z² = 1, as shown in the figure below: z² + y² + z² = 1 (a) Using rectangular coordinates, set-up the triple integral that represents the volume of the solid S. (b) Using cylindrical coordinates, set-up the triple integral that represents the volume of the solid S. (c) Using spherical coordinates, find the volume of the solid S.
4. Let S be the solid that lies above the cone z = /r² + y² and below the sphere r² + y² + z² = 1, as shown in the figure below: z² + y² + z² = 1 (a) Using rectangular coordinates, set-up the triple integral that represents the volume of the solid S. (b) Using cylindrical coordinates, set-up the triple integral that represents the volume of the solid S. (c) Using spherical coordinates, find the volume of the solid S.
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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Transcribed Image Text:4. Let S be the solid that lies above the cone z = Vr2 + y? and below the sphere r? + y? + 22 = 1, as
shown in the figure below:
2² + y? + z2 = 1
(a) Using rectangular coordinates, set-up the triple integral that represents the volume of the
solid S.
(b) Using cylindrical coordinates, set-up the triple integral that represents the volume of the
solid S.
(c) Using spherical coordinates, find the volume of the solid S.
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