Re: volume of a pyramid

First, thanks for the reply.

As for the volume, it is a solid that both radial surfaces
have identical radius toward a common origin. All other 4
surfaces are on a straight plane (as opposed to the two
radial surfaces), and their angles with the vertical axis is
known (i.e.g, vector-to-plane angles are known).

So are your equations supposed to calculate the solid volume
as describe above. I will examine the equations too.
Thanks again.

--------
You haven't stated explicitly what shape your image has.
It looks like a solid
defined by projecting a spherical quadrilateral surface
inwards along radial
lines to a smaller spherical quadrilateral. Is that correct?

If so, then its volume can be calculated in terms of the
area of the outer
quadrilateral:

V = a*R/3*(1 – (r/R)^3)

Where R is the outer radius, r the inner radius, and a the
outer area.

As for computing a, it is equal to

a = R^2*(A + B + C + D – 2*pi)

where A, B, C, and D are the four angles in radians at the
four vertices of the
outer quadrilateral.

So your problem becomes that of determined what those
four angles are.
There is no way of determining them without additional
information about
that quadrilateral.

Roger Stafford


.

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