What is the volume of a truncated octagonal based pyramid?

Answer 1

The volume of a pyramidal frustum whose bases are n-sided regular polygons is

where a1 and a2 are the sides of the two bases.

Note: cot(x) = 1 / tan(x)

For example, I was not provided my a's to calculate the volume my pyramidal octagonal frustrum. I was provided only an overal width (let overal width = W) so I had to calculate a1 with this equation:

a1 = W * (√2 / (2 + √2))

Then with the given h I solved for the overal width for the top octagon using trigometry;

Used the same a1 equation but for a2;

Then used this equation to find my volume:

It works, I tried it and proved it with AutoCAD using the command MASSPROP