# Tanks A Lot

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?

### 2 guesses to Tanks A Lot

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• brent

1.8″ for the 1st cube (10.8″ total water height), and then assuming the 2nd cube is placed on the bottom of the tank (instead of on top of the 1st cube) it rises an additional 2.2″ (13″ total height).

• Brent is correct again! 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.