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Find the volume of the sphere in spherical coordinates with radius a by setting f-1 and evaluating V = fff dv (0<0<2π, 0<φ<π, 0

Find the volume of the sphere in spherical coordinates with radius a by setting f-1 and evaluating V = fff dv (0<0<2π, 0<φ<π, 0

Advanced Engineering Mathematics
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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Find the volume of the sphere in spherical coordinates with radius a by setting f=1 and evaluating
**Volume of a Sphere in Spherical Coordinates** To find the volume of a sphere in spherical coordinates with radius \( a \), we utilize the following integral by setting \( f = 1 \): \[ V = \iiint dv \] The bounds for the integration are: - \( 0 < \Theta < 2\pi \) - \( 0 < \phi < \pi \) - \( 0 < \rho < a \) This configuration sets up the integral in spherical coordinates to calculate the volume of a sphere by integrating within these angular and radial boundaries.
Transcribed Image Text:**Volume of a Sphere in Spherical Coordinates** To find the volume of a sphere in spherical coordinates with radius \( a \), we utilize the following integral by setting \( f = 1 \): \[ V = \iiint dv \] The bounds for the integration are: - \( 0 < \Theta < 2\pi \) - \( 0 < \phi < \pi \) - \( 0 < \rho < a \) This configuration sets up the integral in spherical coordinates to calculate the volume of a sphere by integrating within these angular and radial boundaries.
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