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

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

Then the diagonal of the cube is equal to the diameter of the sphere.

diagonal of the cube = 2 $$\times$$ radius of the sphere

diagonal of the cube = 2 $$\times$$ 6

= 12 cm

Let's assume the side of the cube is 'a' cm.

diagonal of the cube = $$\sqrt{\ a^2+a^2+a^2}$$

$$12 = \sqrt{\ 3a^2}$$

$$12= \sqrt{\ 3}a$$

$$\frac{12}{\sqrt{\ 3}}=a$$

a = $$\frac{12}{\sqrt{\ 3}}\times\frac{\sqrt{\ 3}}{\sqrt{\ 3}}\ $$

= $$\frac{12}{3}\sqrt{\ 3}\ $$

side of the cube = $$4\sqrt{\ 3}\ $$ cm