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The answer depends on the orientation of the pipe and the cut.

Even if the cut is vertical, it can be along the axis (length) of the pipe, at right angles to it or at a slant.

If the cut is along the axis, the cross section will be two rectangles where the length of the rectangle is the length of the pipe and the width is the thickness of the pipe. If the pipe has negligible thickness, this may be taken to be two parallel lines.

If the cut is at right angles to the axis then the cross section will be an annulus which, when the thickness is negligible will become a circle.

Finally, if the cut is skew, then you will get ellipses which will collapse to a single ellipse for negligible thickness.

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Q: What cross-section do you get when you give a vertical cut to a circular pipe?
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