GMAT Quiz Question 1: An inverted conical container, full of water, is of height 8 meters. What will be the height of water in the container when it is half-empty? a) 4^3 b) 4 c) 4 (3√4) d) 4 (3√8)?
Asked by Arshad Iqbal 11 months ago
Operations Analyst at WD
Let the required height be h meters.
Let the volume of the container be V cubic meters.
As shown in the diagram above, we have two cones; the smaller cone representing the water present after the container is half full. We can observe that the cone is wider on top (and hence, represents a greater volume). Thus, the water level need not come down to half the height of the cone in order to be half full. Thus, the correct answer must be greater than 82=4 meters.
The two cones are similar in shape and size; hence, their volume ratio is proportional to the cube of their corresponding dimensions (Note: Try to relate this to ratio of areas of similar 2D figures to be square of the ratio of their sides).
Thus, we have:
=>h3=832=(23)32=292=28
=>h=(28)13=(26)13×(22)13=263×413=22×413=44–√3
=>h=4 (4√3) meters
The correct answer is option C.
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