This figure shows the portion of the sphere whose surface area is computed in the example. Video Example) EXAMPLE 1 The curve y = √36x², -1 ≤ x ≤ 1, is an arc of the circle x² + y² = 36. Find the area of the surface obtained by rotating this arc about the x-axis. (The surface is a portion of a sphere of radius 6. See the figure.) SOLUTION We have dy = dx S = = (36-x²)-1/2 -X √ 36x² and so, by this formula, the surface area is - [²^2=Y √/₁ 2лу1 1 = 2 17 1² ² = 25 [₁ + (dx)² dx √36x² 1 + √36x² = 12″ / ²^1 dx -1 x² 36x² √ 36x² dx dx

This figure shows the portion of the sphere whose surface area is computed in the example. Video Example) EXAMPLE 1 The curve y = √36x², -1 ≤ x ≤ 1, is an arc of the circle x² + y² = 36. Find the area of the surface obtained by rotating this arc about the x-axis. (The surface is a portion of a sphere of radius 6. See the figure.) SOLUTION We have dy = dx S = = (36-x²)-1/2 -X √ 36x² and so, by this formula, the surface area is - [²^2=Y √/₁ 2лу1 1 = 2 17 1² ² = 25 [₁ + (dx)² dx √36x² 1 + √36x² = 12″ / ²^1 dx -1 x² 36x² √ 36x² dx dx

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter5: Similar Triangles

Section5.2: Similar Polygons

Problem 7E

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