Posted by ... on Friday, May 18, 2012 at 6:58pm.
A cone shaped container with its vertex at the top and its circular base on the ground is filled to 3/4 of its height with water. What fractional part of the container is filled with water?

math  Reiny, Friday, May 18, 2012 at 7:18pm
consider the unfilled part of the cone.
It will be similar to the original cone but its dimension are 1/4 of the large cone
the volumes of similar shapes are proportional to the cube of their corresponding dimensions
So the volume of the smaller unfilled cone is 1/4^3 or 1/64 of the large cone
so if the height is 3/4 filled with water, that would be 63/64 of the volume of the cone
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