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The radius of the cylinder is half of the diameter, so the radius is 6cm/2 = 3cm.
The formula for the volume of a right circular cylinder is V = πr^2h, where r is the radius and h is the height.
Plugging in the values:
V = 3.14 * (3)^2 * 12
V = 3.14 * 9 * 12
V = 339.12 cm^3
Therefore, the volume of the right circular cylinder is 339.12 cm^3.