Volume of a "conoid"

[Gaetano]

I am a graduate student in Biomechanics and I am trying to measure the volume of a shape that looks like a cone, but with a base that is not a circle. I am calling this shape a "conoid," but I am not sure if that is the correct geometric term.

The base shape is quite irregular (like an aoemba), but I know the area of the base. I also know the perpendicular height between the apex and the base. The apex is not directly below the base, but actually off to the side a bit. The sides of the conoid surface, as you go from the apex to the perimeter of the base, are straight, so the "slices" of the conoid are the same shape as the base, but different sizes.

I'm not artistic, but I made a schematic which you can see here: Loading Image...

Anyway, can someone tell me the formula for this volume? Is it the same as a cone, 1/3*base area*height? Or is it something else?

Thanks,
Guy

[Lee Rudolph]

Post by Gaetano
Anyway, can someone tell me the formula for this volume?
Is it the same as a cone, 1/3*base area*height?

Yes. (Imagine gathering together all the "stuff" that
makes up the base into a circular disk in an area-preserving
way, and simultaneously--slice by slice--doing that at all
the levels between the base and the apex.)

Lee Rudolph