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Math Help - Washer Method- Inner and Outer Radius?

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    Washer Method- Inner and Outer Radius?

    I am in Calc II and a few days ago we did the section on the disk/washer method. I get how to use the volume formula and integrate just fine, what I don't quite understand is how to obtain the inner and outer radius? I mean, I "get" what they are, sort of, but not when it comes to the actual problems and how to find them. I had this one question in my homework that is a pretty good example of what I'm talking about.

    Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line y=4.

    y= 3/(1+x), y=0, x=0, x=3


    I know in the solutions book they say R(x)=4 and r(x)= 4-3/(1+x), but why? I'm just not understanding how they are finding this? I have tried various things, and while they'll work in one problem, they won't work in the next. I'm not exactly sure what I'm not "getting" (because it seems like it should be awfully simple...), but I just can't get it. I have looked through all of the examples and through my class notes (I have a very vague professor if you haven't guessed...), and I can't find anything that really gets me to understand. Any help would be awesome!
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    Quote Originally Posted by Chinnie15 View Post
    I am in Calc II and a few days ago we did the section on the disk/washer method. I get how to use the volume formula and integrate just fine, what I don't quite understand is how to obtain the inner and outer radius? I mean, I "get" what they are, sort of, but not when it comes to the actual problems and how to find them. I had this one question in my homework that is a pretty good example of what I'm talking about.

    Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line y=4.

    y= 3/(1+x), y=0, x=0, x=3


    I know in the solutions book they say R(x)=4 and r(x)= 4-3/(1+x), but why? I'm just not understanding how they are finding this? I have tried various things, and while they'll work in one problem, they won't work in the next. I'm not exactly sure what I'm not "getting" (because it seems like it should be awfully simple...), but I just can't get it. I have looked through all of the examples and through my class notes (I have a very vague professor if you haven't guessed...), and I can't find anything that really gets me to understand. Any help would be awesome!
    you really need to sketch a diagram ... starting at the axis of rotation, draw the respective radii to the outer and inner boundaries of the region.

    in this case, the length of each radii is the distance from the top function to the bottom function, or top - bottom ...

    R = 4 - 0

    r = 4 - \dfrac{3}{1+x}

    in the case of radii for horizontal revolutions, it's right - left.
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