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

1 answer  ·  posted 2mo ago by JRN‭  ·  last activity 2mo ago by JRN‭

Question volume Reuleaux-triangle surface-of-revolution
#1: Initial revision by user avatar JRN‭ · 2024-10-11T07:17:59Z (2 months 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