SOLUTION: find what fraction of the altitude of a tetrahedron must be cut off by a plane parallel to the base of the tetrahedron such that the volume of the cut off tetrahedron is one third

Question 1088524: find what fraction of the altitude of a tetrahedron must be cut off by a plane parallel to the base of the tetrahedron such that the volume of the cut off tetrahedron is one third of the original volume.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Compared to the original tetrahedron, the smaller tetrahedron cut off is a similar shape, meaning a scaled-down version.
For similar shapes, the ratios of lengths (L and l), surface areas (A and a), and volumes (V and v) are related by
and .
In this case, if is the fraction of the altitude of a tetrahedron cut off by a plane parallel to the base of the tetrahedron,
and the volume of the small cut off tetrahedron is one third of the original volume,
--> .
The exact result is an irrational number, so it cannot be expressed as a fraction.
However, the fractions and are good approximate values.
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