Final answer:
The area cut off is 144 cm² and the volume of the cube is 1728 cm³.
Step-by-step explanation:
To find the area cut off, we need to calculate the area of the square pieces that were cut out from each corner. Since the side length of the square sheet is 12 cm, and we cut out squares from each corner, the side length of the cut-out squares is also 12 cm.
The area of each cut-out square is given by A = s^2, where s is the side length. So, the area cut off is 12^2 = 144 cm^2.
To find the volume of the cube, we need to calculate the side length of the remaining piece and then use the formula V = s^3, where V is the volume and s is the side length. The remaining piece has a side length of 12 - 2(12) = 12 - 24 = -12 cm, but we can ignore the negative sign. So, the side length of the cube is 12 cm, and the volume is 12^3 = 1728 cm^3.