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The Ship in a Tub Problem - part 2

A toy ship is floating in a cylindrical container 10 centimeters in diameter that is partially filled with water.

If a silver teddy bear weighing 100 grams falls off the ship and sinks to the bottom of the container while the ship continues to float, how much will the level of the water rise compared to the original level with just the ship? By the way, silver has a density of 10.49 g/cc.


The silver bear displaces an amount of water corresponding to its volume when it sinks. Since the bear weighs 100 grams and the density of silver is 10.49 g/cc, the volume of the bear and, therefore, the volume of water displaced is 100 g / (10.49 g/cc) = 9.53 cc.

The volume of the cylinder is V=πr2h, where r = 5 cm. The change in water level caused by a volume change V of 9.53 cc is:

h = V/(πr2) = 9.53 cm3 / (3.1416 × 25 cm2) = 0.12 cm

The level of the water will go up by only 0.12 centimeters (1.2 millimeters).

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