# Water Cubes

Bonus unsolved riddle

originally published on April 25, 2011

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

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### 6 guesses to Water Cubes

• tashi

9+12+12=33inch from the bottom the tank

• Dude

That’s not it. Check your math and keep trying.

• Paul

The water will rise from 9 inches to 10 and 1/2 inches after the first cube and up to 12 inches after the second cube.

• Dude

Close, but no.

Keep trying.

• nix

after first: 10 4/5 inch.
after second: 13 inch

• Dude

You nailed it, Nix!

1.8 inches and then another 2.2 inches are the correct increases.

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 rising 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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