Question: [Section 8.1, Arc Length and Surface Area] Observer h R-h IZ R a) Show that...

 

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Question: [Section 8.1, Arc Length and Surface Area] Observer h R-h IZ R a) Show that the surface area of a spherical cap of height h and radius R is 27 Rh. b) Suppose you are at a height d above a sphere of radius R. Show that the portion of the sphere's surface that you can see has area 2π (Hint: Use the results of part a and the triangles in the picture) dR² d+R* c) Suppose the observer moves off to infinity (i.e., doo). What would you expect the limiting value of the observed surface area to be? Check your guess by computing the limit directly, using your result from part b. Question: [Section 8.1, Arc Length and Surface Area] Observer h R-h IZ R a) Show that the surface area of a spherical cap of height h and radius R is 27 Rh. b) Suppose you are at a height d above a sphere of radius R. Show that the portion of the sphere's surface that you can see has area 2π (Hint: Use the results of part a and the triangles in the picture) dR² d+R* c) Suppose the observer moves off to infinity (i.e., doo). What would you expect the limiting value of the observed surface area to be? Check your guess by computing the limit directly, using your result from part b.

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Som 11 Putind PAV 2 x 1115 x RX 5 X 20 384 845 ... View the full answer