Solved: Flux across hemispheres and paraboloids Let S be
Chapter 14, Problem 55(choose chapter or problem)
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 - 1x2 + y22>a, for z 0, where a 7 0. Assume the surfaces have outward normal vectors. a. Verify that S and T have the same base 1x2 + y2 a22 and the same high point 10, 0, a2. b. Which surface has the greater area? c. Show that the flux of the radial field F = 8x, y, z9 across S is 2pa3. d. Show that the flux of the radial field F = 8x, y, z9 across T is 3pa3>2.
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