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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 -

    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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