How to Find Volume with Density – Archimedes Principle

What Is Archimedes Principle?

Archimedes principle was discovered by the greatest mathematician of classical antiquity and one of the greatest of all time i.e Archimedes of Syracuse.

He discovered that when a body is either fully or partially submerged in a fluid, an upward force called buoyant force is exerted on a body immersed in a fluid, which is equal to the weight of the fluid displaced by the body.

In other words, you can say that Archimedes showed how to calculate the volume immersed in fluid.

That’s why this law of floatation is also known as the Archimedes principle of buoyancy. Well, In his Archimedes’ treatise On Floating Bodies, he suggested that:

Any object, wholly or partially immersed in a stationary fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.


History Of Archimedes Principle

Frankly speaking, it’s quite an interesting story. As history narrate us, once Archimedes was asked by the crown prince “King Hiero II of Syracuse” to diagnose that whether the goldsmith had used some silver or any kind of alloy while making his crown.

In other words, he was asked to determine that if a crown was made of gold or any kind of cheaper alloy? Therefore, Archimedes had to find the solution to determine if the goldsmith had embezzled gold during molding the royal crown for the “King Hiero II of Syracuse”. Simply because the order was directed by the king himself.

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Hence, for Archimedes, the easiest way to check the thug of a goldsmith would be determining the density (mass per unit volume) of the crown.

Well, Archimedes could have easily determined the mass of the crown by using measuring scales. But he could not determine the volume of the crown. Simply because he had to solve the mystery without damaging the crown.

That’s why he could not melt the crown into a regularly shaped body to calculate its density. Because if he would damage the crown then he too had to face the wrath of the king. He was baffled by his own thoughts to solve the riddle given by the “King Hiero II of Syracuse”.


Eureka – I Found It

One day, the frustrated Archimedes was about to take a bath. Therefore, when he gets himself into the bathtub. He observed that the level of water increased when he himself entered the bathtub. In other words, he observed that the upward force exerted by a fluid on an object floating in it.

He was completely shocked by his observation. As a result, he didn’t even recognize that he was running naked on the street shouting Eureka (a Greek word meaning “I found it”).

Archimedes discovered the principle when he stepped into a bathtub and the water overflowed/Credit: Wikimedia Commons

In other words, for experimental purposes; water is an incompressible fluid. Therefore, if he submerges the crown in the bathtub. In return, he could easily calculate the volume of the crown based on how much water had been displaced.

In another word, in order to obtain the density of the crown, all he need to do was dividing the mass of the crown by the volume of water displaced. As it was easier to calculate the volume and density of an object if you know the object’s weight.

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Therefore, by using the Archimedes principle he finally determined that the goldsmith actually mixed any other metal with gold while making the crown.

The result of that experimental observation by the great Archimedes is known to as the Archimedes principle. As of now, the Archimedes Principle is a fundamental law of Fluid Mechanics. This is how Archimedes found how to find volume with density. And, the rest is history…!!!

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I am a mechanical engineer by profession. Just because of my love for fundamental physics, I switched my carrier, and therefore I just completed my postgraduate degree in physics. Right now I am a loner (as like ever) and a Physics blogger too. My sole future goal is to do a Ph.D. in theoretical physics, especially in the field of cosmology. Because in my view, every part of physics comes within the range of cosmology. And I love traveling, especially the Sole one.

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