?Use the transformation, x = au, y = av, z = cw and spherical coordinates to show that

Chapter 5, Problem 412

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Use the transformation, x = au, y = av, z = cw and spherical coordinates to show that the volume of a region bounded by the spheroid \(\frac{x^{2}+y^{2}}{a^{2}}+\frac{z^{2}}{c^{2}}=1\) is \(\frac{4 \pi a^{2} c}{3}\) .

Text Transcription:

x^2 + y^2 / a^2 + z^2 / c^2 = 1

4 pi a^2 c / 3

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