So the diagonal length is from an upper vertex to one lower and on the opposite side.
Diagonal Length is sqrt(3).
3 spheres touch across this length. Each sphere has a diameter of 2r. Making a total of 6r to get from that vertex to the other.
Diagonal length = 6r
sqrt(3) = 6r
sqrt(3) /6 =r
sqrt(3)/6 = 0.2886751345948129
radius is about 0.29 in.
How did you get your answer?