Diagonal of the cube = 10*sqrt (3)

Diameter of Sphere = 10 cm

Diagonal of the cube will cross the center of sphere and it is perpendicular on the surface of sphere.

Smallest distance is the perpendicular distance from a surface

If we subtract diameter of sphere from diagonal of cube , we will get the part of diagonal which is out of the sphere.

since it contains two sides

minimum distance = (10 sqrt(3) - 10)/2 = 5*sqrt(3) - 5

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