8. (a) Compute the Jacobian of the change of variables from spherical coordinates to rectangular coordinates. (b)
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8.
(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 Exercise 3, p.
393, and Exercise 7), verify the following classical formulas: the volume of a sphere of radius r is ~7rr3, and the volume of a right circular cone of altitude h and radius r is 7rr2 h/3.
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