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Q&A Volume enclosed by the surface of revolution of a Reuleaux triangle

1 answer  ·  posted 7d ago by JRN‭  ·  last activity 7d ago by JRN‭

Question volume Reuleaux-triangle surface-of-revolution
#1: Initial revision by user avatar JRN‭ · 2024-10-11T07:17:59Z (7 days ago) 
Volume enclosed by the surface of revolution of a Reuleaux triangle
A [Reuleaux triangle](https://mathworld.wolfram.com/ReuleauxTriangle.html) is "a curve of constant width constructed by drawing arcs from each polygon vertex of an equilateral triangle between the other two vertices."

What is the volume enclosed by the surface of revolution of a Reuleaux triangle (with width $w$) through one of its symmetry axes?
volume Reuleaux-triangle surface-of-revolution