Prove that the portion of a sphere of radius R seen by an observer located at a distance
Chapter 8, Problem 54(choose chapter or problem)
Prove that the portion of a sphere of radius R seen by an observer located at a distance d above the North Pole has area A = 2dR2/(d + R). Hint: According to Exercise 48, the cap has surface area 2Rh. Show that h = dR/(d + R) by applying the Pythagorean Theorem to the three right triangles in Figure 22.
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