The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius and h is the height.
Substituting the given values, we get:
V = (1/3)π(3²)(2)
V = (1/3)π(9)(2)
V = (1/3)π(18)
V = (6/3)π
V = 2π
Therefore, the exact volume of the cone is 2π cubic meters.