Final answer:
The difference in the area of one face of the second cube and the area of one face of the first cube is 144 cm².
Step-by-step explanation:
The difference in the area of one face of the second cube and the area of one face of the first cube can be found by subtracting the area of the first cube from the area of the second cube.
The formula for the surface area of a cube is SA = 6s², where s is the length of the side of the cube.
Given that the side of the first cube is 5 cm (since the volume is 125 cm³), the area of one face of the first cube is 6(5)² = 150 cm².
Given that the side of the second cube is 7 cm (since the volume is 343 cm³), the area of one face of the second cube is 6(7)² = 294 cm².
Therefore, the difference in the area of one face of the second cube and the area of one face of the first cube is 294 cm² - 150 cm² = 144 cm².