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First, calculate the area of the base of the cylinder:
A = πr^2
A = 3.14 * 3^2
A = 3.14 * 9
A = 28.26 cm^2
Next, calculate the volume of the cylinder:
V = A * h
V = 28.26 * 6
V = 169.56 cm^3
Therefore, the volume of the cylinder is 169.56 cubic centimeters.