a) Assuming that the center of the rotating circle is at the point (R,0,0) and t

Question

a) Assuming that the center of the rotating circle is at the point (R,0,0) and that the radius of the circle equals r, show that the equation of a torus in cylindrical coordinates is of the form

z= ±r2−(r−R)2−−−−−−−−−−√

b) Set up an integral in cylindrical coordinates for the volume of a torus as above and

show that its volume equals 2Ï€2r2R2

Hint: use substitution to solve the double integral. This will give you one easy integral and one very symmetric one.

(Please show work)

Explanation / Answer

Please refer to my site link

http://whistleralley.com/torus/torus.htm

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~ Swami Vivekananda

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