Water Poured Into Liter Cube

Water is poured at a constant rate into a one-liter cube near its corner. The water rises to the halfway mark, stops for a moment, and then continues to rise at exactly half its previous rate. The reason is that inside the cube is a hollow cylindrical can that has been attached to the bottom. What are the height and radius of the can? (Recall that a one-liter cube measures 10 cm on each edge.)


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What happens is that the water rises until it gets to the top of the can, then it stops rising while the can fills up, and then it continues at half its previous rate. This last means that the cross-section of the can is half that of the cube, that is,
pir2 = 102 / 2 = 50.

So, pir2 = 50 → r = √50 / pi ≈ 3.99 cm. Since the water level stops rising halfway up the cube, the can must be 5 cm high.

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