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Intermediate

The axe head

A tetrahedron with given vertex coordinates. What is its volume?

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Solution

The volume is 20.

Solution by Peter Reusens.

The volume is symmetrical about the y=0 plane. Also AB is orthogonal to the y=0 plane. Thus we have two tetrahedra sharing a base triangle ECD and heights EA=EB=2. Filling the coordinates, the base triangle has surface 15, × 1/3 × height. 15×[1/3]×4 = 20.

Poem

The axe is greedy
It bites the trees
It cuts the wood
And it frightens me !
The woodcutter works
With it all day long
From roots to canopy
Roaring with it’s saw
Or wields his axe fiercely
Life is not so easy
Sometimes much stress
But there is no mercy
He cuts and hacks the trees

Bella

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