A cone-shaped container is oriented with its circular base on the top and its apex at the bottom. I'm confused with this one...

The water will reach a height of 2 inches creating a similar cone. Since the ratio of the height of the smaller to the larger cone is 2:6 or 1:3, that means that the radius of the cones are in a ratio of 1:3 meaing the smaller cone has a radius of 6. Knowing this, the volume of a cone is 1/3Bh, where B is area of base and h is the height so we get 1/3*36pi*2= 24 pi.

Hope it helps!

The fast way to do it is to realize that the ratio of corresponding side lengths is 1 to 3. The ratio of volumes of similar shapes is ration of sides cubed. So the ratio of the volumes would be 1^3 to 3^3 or 1 to 27.

So if the large cone has a volume of 648pi, then 648pi/27= 24pi. This is a neat trick to know and works with area as well.

Hope it helps!

Note  that  the  small  cone formed  by the water  is similar to the  larger cone

The scale  factor  for the small cone to the large cone =   2 / 6  =  1/3

The  fraction of the  volume of the cone when  filled to 2 in = scale factor^3 =  (1/3)^3  =  1/27