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Area of a Surface of Revolution

Area of a Surface of Revolution. For a cylinder, the area is So, if we have an infinitesimally long (tall) cylinder, its area is. w here l is the length of the arc. This gives us a surface area (if our function is rotated about the x-axis) of. The radius is:

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Area of a Surface of Revolution

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  1. Area of aSurface of Revolution

  2. For a cylinder, the area is So, if we have an infinitesimally long (tall) cylinder, its area is where l is the length of the arc.

  3. This gives us a surface area (if our function is rotated about the x-axis) of The radius is: If the function is described as x = g(y), then it’s

  4. If our function is rotated about the y-axis, the surface area becomes For a function described as x = g(y), we have

  5. Example: The curve is an arc of the circle Find the area of the surface obtained by rotating this arc from about the x-axis.

  6. Example: The arc of the parabola from (1,1) to (2,4) is rotated about the y-axis. Find the area of the resulting surface.

  7. Homework p. 559 #1, 3, 5, 11, 15

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