Calculate the volume of the solid bounded by the sphere x2 + y2 +z2 =4 and the cylinder x2 + ( y - 1 )2 = 1
Calculate the volume of the solid bounded by the sphere x2 + y2 +z2 =4 and the cylinder x2 + ( y - 1 )2 = 1
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.CR: Review Exercises
Problem 22CR
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Question
Calculate the volume of the solid bounded by the sphere x2 + y2 +z2 =4 and the cylinder x2 + ( y - 1 )2 = 1
Expert Solution
Step 1
Triple integral is used to find the volume of a solid in three dimension. Sometimes, it is very critical to find the integral using the Cartesian coordinate system. In that case, use of cylindrical coordinate system is convenient. In this coordinate system, the point is converted to . Then, the volume in cylindrical coordinate is formulated as
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