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Topic: Three Sided Pyramid Volume Question.
Replies: 2   Last Post: Nov 9, 2017 12:08 PM

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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
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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




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