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How to Measure Glass With Archimedes' Principle

Tradition has it that Archimedes came upon his principle of buoyancy when seeing the water level rise as he stepped into the bathtub. So excited was he by the discovery, he supposedly ran through the streets naked. And though this origin story may be hyperbolic, Archimedes' principle of buoyancy is laid out in Book One of his "On Floating Bodies" work and can be summarized as, "Any object in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object." The corollary of this principle is that the volume of the displaced fluid equals the volume of a submerged object. By this principle, you can easily make a close measurement of a glass' volume and density with some everyday tools.

Things You'll Need

Plastic, rectangular container big enough to fit your piece of glass completely inside
Tape measure
Scale

Instructions

- 1
  Weigh your dry piece of glass with your scale and record the value. Make sure the scale is properly zeroed first.
- 2
  Fill your plastic container with enough water that it will completely submerge the glass without overflowing.
- 3
  Measure and record the horizontal sides of the interior of the box by laying the tape measure over top of the container and subtracting for the thickness of the actual sides of the box.
- 4
  Measure and record the depth of the water by putting the tape measure into the water so that the end is flush with the bottom and that it is running straight up.
- 5
  Multiply the three values together to find the volume of the water. Write this value down for later.
- 6
  Gently submerge your glass in the water without getting any of the water outside of your container. Make sure the glass is fully immersed and that there is still an uncovered section of the bottom.
- 7
  Measure and record the new depth of the water by again putting the tip of the tape measure flush with the bottom of the container.
- 8
  Multiply this new depth by the horizontal measurements of the container to get the total volume.
- 9
  Subtract the total volume from the initial water's volume to find the volume of the glass.
- 10
  To find the density of the glass, divide the weight of the glass that you found by weighing it in the beginning by its volume that you just found.

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