A cube of maximum possible volume is removed from a solid wooden sphere of radius 6 cm. The side of the cube is:

$4\sqrt{3}$cm

We know that,

Diagonal of cube = \(\sqrt {3}\) × Side of cube

We have,

Radius of the sphere = 6 cm

then, Diameter of the sphere = 2 × 6 = 12 cm

We also know that, Diagonal of cube = Diameter of sphere

\(\sqrt {3}\) × Side of cube = 12

= Side = 4\(\sqrt {3}\)