Glass Marble Gravel

Geometry Level 2

The year is 2190 and water is the most expensive resource on the planet. But you've got a large, cubical tank (~1 cubic meter) that you need to fill with water, or, at least you need to fill the top half of the tank with water. The bottom half can be filled with gravel. So you order two bags of marbles on Amazon, but when they come, they are two different varieties of gravel and way more than you need:

  • Bag 1 contains tiny marble spheres, about 1mm in diameter, almost like sand, and there are enough that you could fill the entire tank.
  • Bag 2 contains large marble spheres, about 3cm in diameter, and there are enough to completely fill the tank.

What should you do to minimize the amount of water that will be wasted in the bottom half of the tank?


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