Three Sided Pyramid Volume Question.

[Simon]

For the record I'm 56, so this isn't homework. :)

I've enclosed a diagram of the problem I'm working for reference.

Start with a cube. All edges are the same value. For reference, the corners of the cube are designated by numbers, the middle point of each edge is identified by a letter. Clear as mud?

I need to take away the corners and determine the volume without them. One corner is determined by lines from A -> D D -> F F -> A

Assuming each edge is 3.720, the middle point (from 1 -> D or D -> 4) is 1.860.

Finding the distance from A -> D is found by simple trig to be 2.63044

The volume of a three sided pyramid can be found with the formula V = 1/3AH
A = area of the triangle base. H = height of the pyramid.

I know A = 2.99611, but how do I find H or the height in that scenario? Once I know that I can multiply corner volume by 8 to get the volume of all eight corners and subtract it from the whole.

Thanks.

Attachment available from http://mathforum.org/kb/forum.jspa?forumID=125

[Simon]

Found the answer using this:

https://rechneronline.de/pi/triangular-pyramid.php

[uuurchin]

Wow, that "Rechner" site has a dizzying array of useful tools -- many, unique.

Thank you for sharing this tip, Simon!