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The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
In this case, the radius is 4 cm (half of the diameter) and the height is 6 cm.
Plugging the values into the formula:
V = 3.14 x 4^2 x 6
V = 3.14 x 16 x 6
V = 301.44 cubic centimeters
Therefore, the volume of the cylinder is approximately 301.44 cubic centimeters, which is not one of the provided answer choices.