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?

Answer 1

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