Volume of a solid of revolution: loop of the Folium of Descartes

Don Cole

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Nov 3, 2016
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problem: Rotate the loop of the Folium of Descartes about its line of symmetry and and calculate the volume of the resulting solid of revolution (SOR). I have managed to do this, I think! My question is, is this a known quantity? Almost every site or information source that I have accessed concerning this famous curve shows how to calculate the area of the loop but none have ever mentioned the volume of the SOR. if the volume is a known quantity, you would think that the methodology of how to get it would be as common as the methodology for the area of the loop. if anybody knows what the volume of this solid is or how to calculate that volume, I would appreciate some discussion here. Thank you.
 
problem: Rotate the loop of the Folium of Descartes about its line of symmetry and and calculate the volume of the resulting solid of revolution (SOR). I have managed to do this, I think! My question is, is this a known quantity? Almost every site or information source that I have accessed concerning this famous curve shows how to calculate the area of the loop but none have ever mentioned the volume of the SOR. if the volume is a known quantity, you would think that the methodology of how to get it would be as common as the methodology for the area of the loop. if anybody knows what the volume of this solid is or how to calculate that volume, I would appreciate some discussion here. Thank you.
Please show us your work so we can see if your correct. What equation are you using for the loop and line of symmetry?
 
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