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a. A torus of revolution (doughnut) is obtained by rotating a circle C in the xz-plane about

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a. A torus of revolution (doughnut) is obtained by rotating a circle C in the xz-plane about the z-axis in space. If C has radius r > 0 and center (R, 0, 0), show that a parametrization of the torus isimage


where 0 ≤ u ≤ 2π and 0 ≤ y ≤ 2π are the angles in the figure.


b. Show that the surface area of the torus is A = 4π2Rr.image


image

Transcribed Image Text:

r(u, v) = ((R+ r cos u)cos v)i + ((R + r cos u)sin v)j + (r sin u)k,

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a To show that the given parametrization represents the torus we need to verify that it satisfies the conditions of a torus The parametrization of the torus is given as ru v R r cos u ...View the full answer


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