A person finds a piece of wood in a shape of irregular tetrahedron with base edges of length: 5, 6, 7 cm and the remaining three edges of length 8 cm.

Because the surface of the wooden block is damaged, the person decides to take 0.5 cm off each face of the tetrahedron. After doing so, he notices further damage near the vertices of the tetrahedron so he decides to make a sphere shape. What is the radius \(r\) of the largest sphere he can make of the remaining wooden block?

Submit your answer as \(\lfloor 10000r \rfloor\).

Try also Woodworks II

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