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Difficulty: MediumPuzzle Details

The area of the floor of the tank is 6 square feet, and the water in it is 9 inches deep. How much does the water rise if a 1-foot metal cube is placed in it? How much further does the water rise if a second 1-foot cube is also placed in the tank?

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[Ref: ZRLN]  

Answer: 1.8 inches, then another 2.2 inches.

Initially the volume of water is 6 * 9/12 = 4.5 cubic feet. The first cube effectively reduces the cross-sectional area of the tank to 5 square feet, causing the water to be 4.5/5 foot = 10.8 inches deep. Therefore rises 1.8 inches. The second cube is then placed on the floor of the tank, the cross-sectional area is 4 square feet up to a height of 1 foot, and this is filled by 4 cubic feet of water. The remaining 0.5 cubic foot, in a cross-sectional area of 6 square feet, requires a height of 0.5/6 foot = 1 inch. The water is therefore 13 inches deep and has risen by another 2.2 inches.


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