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
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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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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