I don't know if the part about Archimedes running naked through town is true, nor do I know how things turned out regarding the crown and the goldsmith. What I do know is you can use Archimedes' idea to calculate the volume of an object, and its density, if you know the object's weight. For a small object, in the lab, the easiest way to do this is to partly fill a graduated cylinder large enough to contain the object with water (or some liquid in which the object won't dissolve). Record the volume of water. Add the object, being careful to eliminate air bubbles. Record the new volume. The volume of the object is the initial volume in the cylinder subtracted from the final volume. If you have the object's mass, its density is the mass divided by its volume.
Most people don't keep graduated cylinders in their homes. The closest thing to it would be a liquid measuring cup, which will accomplish the same task, but with a lot less accuracy. There is another way to calculate volume using Archimede's displacement method. Partially fill a box or cylindical container with liquid. Mark the initial liquid level on the outside of the container with a marker. Add the object. Mark the new liquid level. Measure the distance between the original and final liquid levels. If the container was rectangular or square, the volume of the object is the inside width of the container multiplied by the inside length of the container (both numbers are the same in a cube), multiplied by the distance the liquid was displaced (length x width x height = volume). For a cylinder, measure the diameter of the circle inside the container. The radius of the cylinder is 1/2 the diameter. The volume of your object is pi (3.14) multiplied by the square of the radius multiplied by the difference in liquid levels (pr2h).
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