The following question was asked in the comments section of the article Archimedes' Principle Explained.

**Q:**Can you just explain how to measure the volume of an irregularly shaped object which floats in water? Can we use Archimedes' principle? How?

**A:**It is certainly possible to do so using Archimedes' principle, provided the density of the object is known. The key here is to find the mass of the object. Then we use the mass formula Mass =

*Vρ*(where

*V*is the volume of the object and

*ρ*is the density of the object) to find the volume.

In my article Archimedes' Principle Explained, there is a section about objects floating freely. It is mentioned that

Weight of floating body = Weight of fluid displaced

therefore

Mass of floating body = Mass of fluid displaced

So if we can know the mass of water displaced (e.g. measuring the apparent increase in volume of water and multiplying it with its density, as in finding mass using the mass formula) when the object floats in water, we can know the mass of the object.

By rearranging the mass formula and substituting the mass and

*ρ*into it, we can have the volume of the object. However, we must know the value of

*ρ*beforehand.

**Note:**The above answer does not take into account other ways of finding the volume of an object that floats in water other than using Archimedes' principle.

## 4 comments:

What an amazing post. I am a high school senior and have an early admit from Dartmouth College. I am planning to major in Physics. This type of posts are certainly helpful for fundamental queries from time-to-time. Kudos to you!. By the way, i came across these excellent physics flashcards. Its also a great initiative by the FunnelBrain team. Amazing!!!

One of the easier way without doing any calculation is to use a sinker. A sinker is something that can force the irregular object to sink. Using displacement method, find the total volume displaced when the irregular object and the sinker sinks. Take the irregular object out. Let the sinker sinks and know the volume it displaces. Subtract the Volumes. The volume of displaced by the irregular object + sinker) - the volume displaced by the sinker alone. You get the volume of the irregular object. Got it? Vincent@ Spokane community college, WA.

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