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I just took an exam and the question was this:

Find the volume where the base is a triangle with the vertices: (0,0),(4,0),& (0,4). The cross section is a semicircle and is perpendicular to the y-axis and is parallel to the x-axis.

I get everything up to the "parallel to the x-axis" part. Okay, so we are not using the z-axis for this course but isn't the cross-section parallel to the z-axis?

Okay, so I guess the professor was talking about was the base of the cross-section, not the cross-section.

I get that.

However, I have looked around the internet and in my multiple text books and I have never seen this type of problem explained as "parallel to the x-axis" so I want to know if this is incorrect syntax.

If the base is along the x and the y axis, how is the cross-section itself parallel to x?

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  • $\begingroup$ The wording is a bit awkward. The best interpretation (as you seem to suggest) is that "perpendicular to the $y$-axis" describes the plane of the semicircular cross section, while "parallel to the $x$-axis" describes the diameter of the semicircle itself. (For a plane, "perpendicular to $y$" already guarantees "parallel to $x$ (and $z$)", so using both to describe the cross-sectional region would be redundant.) I might've phrased things like this: "Cross sections, in planes perpendicular to the $y$-axis, are semi-circles (above the $xy$-plane) with diameters spanning the figure's base." $\endgroup$
    – Blue
    Commented Oct 15, 2017 at 4:04
  • $\begingroup$ @Blue You see, this is what confused me. I would have understood that. $\endgroup$
    – mchid
    Commented Oct 15, 2017 at 4:15
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    $\begingroup$ @Blue I probably spelled that wrong. My spell check is British English, not U.S. $\endgroup$
    – mchid
    Commented Oct 15, 2017 at 4:16

1 Answer 1

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Why not simpler

A triangle has vertices: O (0,0),X(4,0),& Y (0,4). Find half cone volume enclosed when triangle $YOX$ (slant line and base radius) are rotated $180^0$ about y-axis.

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  • $\begingroup$ I'm not asking how to do the problem, I am asking if it is correct to say that the slices are parallel to the x axis. $\endgroup$
    – mchid
    Commented Oct 14, 2017 at 21:55
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    $\begingroup$ Well, yeah, why not simpler is exactly what I am saying as a student. This professor seems to try to make things way more complicated than they actually are to the point that I don't even think I have really learned any of the actual concepts we should be covering (too focused on dumb stuff like this). Not to mention the fact that the slices are parallel to z and perpendicular to both x and y not parallel to x. The base of the semicircle runs parallel to x, not the slice. $\endgroup$
    – mchid
    Commented Oct 14, 2017 at 22:02
  • $\begingroup$ Yes a problem statement should be brief and yet include all essential features. $\endgroup$
    – Narasimham
    Commented Oct 15, 2017 at 1:51

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