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The article says "... the volumes of the solids generated by revolving the curve around ..." and then gives formulas. When you revolve a curve around an axis you get a surface of revolution with volume 0, not a solid. There should actually be three formulas depending on the actual area being
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vertical (parallel to the y-axis) for functions defined in terms of x and horizontal (parallel to the x-axis) for functions defined in terms of x. both say defined in terms of x. so what's the difference. there's something wrong with this wording. Also, How do you know which "line" to draw?
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This is still not right. For a start, the volume formula doesn't take into account the angle the line segment makes with the axis. --
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the most well-known and the more simple one (direct analogy with π r² (area of circle) resp. × h (volume of cylinder).
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Furthermore, I just noticed that the Dutch version not only gives formulas for the volume, but also for the surface.
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The Dutch page on Solids of rev. is quite good for pictures. Can someone transfer them over here please?
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Current definition: revolving a curve around an axis doesn't give solid, it is the
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I suggest to put the "rotation about the x-axis" before the other one, as it is
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revolved; I'll try to find a source with all three and add them when I do. --
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Can we add details about the center of mass formula or a link to it?
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