The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where r is the radius of the circular base, h is the height of the cone, and π is constant approximately equal to 3.14.
Substituting the given values, we get:
V = (1/3)π(18^2)(6) = 6,084π cubic inches
To find the fraction of the volume of the cone filled when the water reaches a height of 2 inches, we need to calculate the volume of water in the cone. The water will form a smaller cone with a height of 2 inches and a radius of 18 inches.
Using the same formula as above, we get:
V_water = (1/3)π(18^2)(2) = 648π cubic inches
The fraction of the volume of the cone filled with water is then:
V_water / V = (648π) / (6,084π) = 0.106, which is approximately equal to 1/9.
Therefore, the answer is C. 1/9.