a. A torus of revolution (doughnut) is obtained by rotating a circle C in the xz-plane about the z-axis in space. (See the accompa- nying figure.) If C has radius r > 0 and center (R, 0, 0), show that a parametrization of the torus is r(u, v) = ((R + r cos u)cos v)i + ((R + r cos u)sin v)j + (r sin u)k, where 0 s u s 2n and 0 < v < 27 are the angles in the figure. b. Show that the surface area of the torus is A = 47°Rr. R. r(u, v)

a. A torus of revolution (doughnut) is obtained by rotating a circle C in the xz-plane about the z-axis in space. (See the accompa- nying figure.) If C has radius r > 0 and center (R, 0, 0), show that a parametrization of the torus is r(u, v) = ((R + r cos u)cos v)i + ((R + r cos u)sin v)j + (r sin u)k, where 0 s u s 2n and 0 < v < 27 are the angles in the figure. b. Show that the surface area of the torus is A = 47°Rr. R. r(u, v)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 18T

See similar textbooks