Flux across hemispheres and paraboloids Let S be the hemisphere x2 + y2 + z2 = a2, for z ≥ 0, and let T be the paraboloid z = a – (x2 + y2)/a, for z ≥ 2= 0, where a > 0. Assume the surfaces have outward normal
a. Verify that S and T have the same base (x2 + y2 ≤ a2) and the same high point (0, 0, a).
b. Which surface has the greater area?
c. Show that the flux of the radial field F = 〈x, y, z〉 across S is 2πa3.
d. Show that the flux of the radial field F = 〈x, y, z〉 across T is 3πa3/2.
Want to see the full answer?
Check out a sample textbook solutionChapter 17 Solutions
Calculus: Early Transcendentals (3rd Edition)
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (3rd Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Calculus & Its Applications (14th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,