?(a) Evaluate \(\iiint_{E} d V\), where E is the solid enclosed by the ellipsoid \(x^{2}
Chapter 14, Problem 23(choose chapter or problem)
(a) Evaluate \(\iiint_{E} d V\), where E is the solid enclosed by the ellipsoid \(x^{2} / a^{2}+y^{2} / b^{2}+z^{2} / c^{2}=1\). Use the transformation \(x=a u, y=b v, z=c w\).
(b) The earth is not a perfect sphere; rotation has resulted in flattening at the poles. So the shape can be approximated by an ellipsoid with a − b − 6378 km and c − 6356 km. Use part (a) to estimate the volume of the earth.
(c) If the solid of part (a) has constant density k, find its
moment of inertia about the z-axis.
Equation Transcription:
∭
Text Transcription:
triple integral_E dV
x^2 / a^2 +y^2 /b^2 +z^2 /c^2 =1
x=au, y=bv, z=cw
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