Hands-on brainteaser: The boat and anchor challenge

Weight versus volume

When it's in the boat, the anchor displaces a volume of water with the same weight as the anchor itself.

When it's submerged in the water, the anchor displaces an amount of water equivalent to its own volume.

Because the anchor - made of steel, say - is heavier than the equivalent volume of water, it displaces more water when it's in the boat. Submerged, it only displaces its own volume, and all else being equal, the water level falls.

Test it at home

You can easily test this yourself in the kitchen sink, using a sandwich box as the boat, and something like a paperweight as the anchor.

Put a few centimetres of water into the sink (enough to easily cover the paperweight later). Then put the paperweight into the sandwich box, and float the box on the water.

Once the water has settled, mark the water level in the sink with a felt-tip pen. Now take the weight out of the box, and submerge it in the water.

When it's settled again, you'll see that the water level has indeed fallen (the bigger the paperweight, or the less water there is, the more the water level will fall).