SOLUTION: A sphere is inscribed in a regular tetrahedron. If the length of an altitude of the tetrahedron is 36, what is length of a radius of the sphere

Question 548597: A sphere is inscribed in a regular tetrahedron. If the length of an altitude of the tetrahedron is 36, what is length of a radius of the sphere
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
The radius (r) of an inscribed sphere (aka insphere) of a regular tetrahedron with edge length = a, is given by:

The edge length is not given but we do know the altitude or height (h) of the tetrahedron so we can compute the edge length as follows:
and h is given as so...

Now we can find r:
Substitute

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