Answer:
432 square inches
Step-by-step explanation:
The 27 smaller cubes each have a dimension that is 1/∛27 = 1/3 the dimension of the larger cube. That is, each is a 2" cube. Their total surface area is ...
(27 cubes)(6 faces/cube)((2 in)²/face) = 648 in²
The painted surface area of the larger cube is ...
(6 faces/cube)((6 in)²/face) = 216 in²
Subtracting the painted cube area from the total cube area of the smaller cubes, we have an unpainted area of ...
648 in² -216 in² = 432 in² . . . unpainted area
