Volume enclosed by the surface of revolution of a Reuleaux triangle
A Reuleaux triangle 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
1 answer
Shown below is a Reuleaux triangle with the
Let points
A circle centered at
The solid is bounded by the planes
The second integral is
The first integral is
To find
To find
Choose
Thus,
Finally,
For a width
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