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 (pr

^{2}h).

Worked Chemistry Problems | Chemistry Definitions

## Comments

You say:

“Technically, he didn’t even need to weigh the crown, if he had access to the royal treasury, since he could just compare the displacement of water by the crown with displacement of water by an equal volume of the gold the smith was given to use.”

Archimedes still needs the mass (or weight at the same place on Earth) of the gold. — If the goldsmith replaced pilfered gold with an equal volume of lead, for instance, and mixed it well with the remaining gold, there is no way to tell feom the volume displaced without the mass as well. The DENSITY, requiring both mass AND volume, of the crown gives the answer, not the volume alone.

Dactual = Mair/(Mair-Mwater) Or simply stated the density of an object is equivalent to the mass in air divided by the difference between its mass in air and its mass in water.

“Technically, he didn’t even need to weigh the crown, if he had access to the royal treasury, since he could just compare the displacement of water by the crown with displacement of water by an equal volume of the gold the smith was given to use.”

You are correct in saying that it is not necessary to know the weight of the crown to know if this is gold, however, the way it is described is simply wrong.

If you replace a metal by another metal occupying the same volume, they will both displace the same volume of water. On the other hand, if you can compare the displacement of water of the crown to the displacement of water of the same weight of gold (knowing the exact weight is irrelevant to the problem) from the treasury. If the displacements are equal the crown is made of gold.

One could imagine having a mixture of metals with an average density equal to the density of gold. Only tungsten’s density is very close to gold’s density, and platinum’s is higher. If it is platinum don’t say anything and wear it proudly

this didn’t tell me how to measure my body fatat all you idiot thanks to you i still eat twinkies for breakfast1 $#@$%@$

Actualy the King got another Crown and the goldsmith head was chopped off for trying to trick the king.

lmfao!!!!!!!!

How did he do it????

i think this is helpful, though some parts are difficult to work out what is meant. thank-you!

he actually said Eureka for some thing else!!!!!!!!!!!!!!!

hi mam,

Please tell how do i check a hollow gold balled ornament using density test. Or any other way to identify the balled ornament is gold ? please reply me

How did he do it because its confusing Me….