Math Is Fun Forum

samuel.bradley.99

Member

Registered: 2016-03-16

Posts: 51

Truncated tetrahedron

Given a tetrahedron IABC where all its edges have equal length x, we take points A1 on IA, such as IA1=1/2 IA, point B1 on IB such as IB1=2/3 IB and point C1 on IC such as IC1=3/4 IC.
Find the volume of tetrahedron IA1B1C1 in relation to a.

Sorry, I accidentally cut off half the wording

Last edited by samuel.bradley.99 (2017-07-31 00:47:58)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,608

Re: Truncated tetrahedron

hi samuel.bradley.99

I've been away so I've only just seen this problem.  I had a vague memory that the volume of a tetrahedron could be calculated using vector cross and dot products.  A quick 'google' took me to this page:

https://math.stackexchange.com/question … ot-product

Your tetrahedron is a regular one by the way which fixes the directions of the vectors IA, IB and IC.  So it looks like you can use this formula to get a result.  But post back if you need a quick lesson in cross and dot products. 

Bob

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Children are not defined by school ...........The Fonz
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Sometimes I deliberately make mistakes, just to test you!  …………….Bob