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Simon
Posts:
4
From:
Bermuda
Registered:
11/8/17


Three Sided Pyramid Volume Question.
Posted:
Nov 8, 2017 2:44 PM


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.
Imgur image here: https://i.imgur.com/3MHHXRL.jpg



