A cone-shaped container is oriented with its circular base on the top and its apex at the bottom. It has a radius of 18 inches and a height of 6 inches The cone starts filling up with water.What fraction of the volume of the cone is filled when the water reaches a height of 2 inches? (1)/(729) (1)/(27) (1)/(9) (1)/(3)

## Step 1:The volume of a cone is given by the formula , where is the radius of the base and is the height.## Step 2:The volume of the cone when it is filled with water to a height of 2 inches can be calculated using the same formula, but with a height of 2 inches and a radius that is proportionally smaller. Since the height is one-third of the total height, the radius of the water-filled portion is also one-third of the total radius, or 6 inches.## Step 3:Calculate the volume of the entire cone and the volume of the water-filled portion. ## Step 4:The fraction of the volume of the cone that is filled with water is given by the ratio .### \( V_{cone} = \frac{1}{3} \pi (18)^2 (6) \)### \( V_{water} = \frac{1}{3} \pi (6)^2 (2) \)### \( \frac{V_{water}}{V_{cone}} = \frac{\frac{1}{3} \pi (6)^2 (2)}{\frac{1}{3} \pi (18)^2 (6)} \)