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a) Compute the Jacobian of the change of variables from spherical coordinates to rectangular coordinates.
b) Assuming that Vol is translation and rotation invariant (see Exercises 12.1.7 and 12.4.7), verify the following classical formulas: the volume of a sphere of radius r is 3/4πr3, and the volume of a right circular cone of altitude h and radius r is πr2h/3. |
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