DIY Speaker With Curved Sided Cabinet

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After seeing these images of a DIY build, bringing back memories of the Wilson Benesch speakers that I really loved the look of in the late 90's I'm interested in looking at doing my own curved wall design.

I'm digging around for more information, but does anyone know how to calculate the changes in volume using this profile?

Is there an online calculator or formula or is it just a question of trying to "cut up" the profile into known geometric shapes and working out the surface area?
 

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