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How can the volume of a square-crosssection prism that is curved with the following dimensions be calculated?

  • inner $R$ radius
  • with squared section area $a \cdot a = S$
  • length is an arc of longitude $L$

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Álvaro Franz
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    Is the radius of curvature on the inside, the outside or the center of the prism? – Prime Mover May 19 '21 at 10:25
  • @PrimeMover Inside, thanks for the attention – Álvaro Franz May 19 '21 at 10:29
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    As long as the "section" at different part of solid doesn't intersect and the locus of centroid is a regular enough curve, the volume is the area of section times the length of the locus of centroids. This works even if you twist the section around the centroid as it moves along the locus. – achille hui May 19 '21 at 10:46
  • @achillehui This together with GoRza's answer is the perfect combination. Thank you! – Álvaro Franz May 19 '21 at 13:30
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    Hmm... thinking about it, I missed a condition in previous comment, the section need to be perpendicular to the tangent vector of the locus of centroids for the formula to work (which holds in your case) – achille hui May 20 '21 at 23:29

1 Answers1

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HINT

You can calculate the area of the basis (the "curved band") and then multiplicate by the high.

GoRza
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