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First, we need to find the area of the entire compact disc by using the formula for the area of a circle: A = πr^2.
Given that the diameter of the compact disc is 120 millimeters, we can find the radius by dividing the diameter by 2: 120 mm / 2 = 60 mm.
Next, we can plug the radius into the formula for the area of a circle and calculate the area: A = 3.14 x (60 mm)^2 = 3.14 x 3600 mm^2 = 11,304 mm^2.
Therefore, the approximate area of the compact disc, ignoring the center hole, is approximately 11,304 mm^2, which corresponds to option A.