3 g of paint was used to paint the wooden cube. When it was dry, the cube was cut into 27 equal smaller cubes.

3 g of paint was used to paint the wooden cube. When it was dry, the cube was cut into 27 equal smaller cubes. How much paint is required to paint over the resulting unpainted surfaces?

Let the length of the edge of the large cube be equal to a.

Then the volume of the cube is V = a ^ 3, and the surface area is S = 6a ^ 2.

The volume of the small cube is v = V / 27. The side of the small cube is b = (V / 27) ^ 1/3 = (a ^ 3/27) ^ 1/3 = a / 3.

The surface area of the small cube is s = 6b ^ 2 = 6 * (a / 3) ^ 2 = 6a ^ 2/9.

The total area of all small cubes is 27s = 27 * (6a ^ 2/9) = 18a ^ 2. The area S = 6a ^ 2 is already painted. It remains to paint

18a ^ 2 – 6a ^ 2 = 12a ^ 2.

If 3 g of paint was spent on an area of 6 a ^ 2, then 6 g of paint will be required for an area of 12a ^ 2.

Answer: 6 g of paint.