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Given that the volume of the cube is 512 cubic cm, we can start by finding the length of one side of the cube.
The formula for the volume of a cube is:
Volume = side^3
Since the volume is given as 512 cubic cm, we can set up the equation:
512 = side^3
To solve for the side length, we can take the cube root of both sides:
∛512 = ∛(side^3)
8 = side
Now that we have determined that the side length of the cube is 8 cm, we can find the area of one face, which is the area of a square with side length 8 cm.
The formula for the area of a square is:
Area = side^2
Plugging in the side length of 8 cm, we have:
Area = 8^2 = 64 square cm
Therefore, the area of one face of the cube is 64 square cm.