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Math Help - Parametric Equations Problem

  1. #1
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    Parametric Equations Problem

    I am a bit confused about how to set up this problem:

    A cow is tied to a silo with radius 6 by a rope just long enough to reach the opposite side of the silo. Find the area available for grazing by the cow. The rope must be 6pi in length, but I am not sure what to do with it from there.

    I need to know how to solve this via parametric equations. Any help would be appreciated. Thanks.
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  2. #2
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    Quote Originally Posted by machi4velli View Post
    I am a bit confused about how to set up this problem:

    A cow is tied to a silo with radius 6 by a rope just long enough to reach the opposite side of the silo. Find the area available for grazing by the cow. The rope must be 6pi in length, but I am not sure what to do with it from there.

    I need to know how to solve this via parametric equations. Any help would be appreciated. Thanks.
    Draw a picture. The required area is the area inside the larger circle (radius
    6 pi) and outside the smaller (radius 6).

    A = pi (6 pi)^2 - pi 6^2 = 36 pi (pi^2 -1).

    RonL
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  3. #3
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    The rope is attached to a point on the outside of the silo (sorry, I didn't explain it well), so the outline of the shape formed by the outstretched rope does not form a circle. It makes a semicircle on one side but on the other the rope wraps around the silo and returns to a point on the opposite side of the silo, it looks similar to the graph of the polar equation r = 1 + cos(theta)
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