Question: USING PYTHON PROGRAM Rotating the circle (xR)2+y2 = r2 about the y axis creates a torus. (R > r for this to make sense). (a)

USING PYTHON PROGRAM

Rotating the circle (xR)2+y2 = r2 about the y axis creates a torus. (R > r for this to make sense).

(a) Use slicing to set up and evaluate an integral to nd the volume of the torus. Simplify.

(b) Use method of cylindrical shells to set up and evaluate an integral to nd the volume of the torus. (HINT: If Python cannot integrate directly, make an appropriate substitution by hand, then try integrating the result).

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