# What is the volume of cavities?

1. Feb 9, 2005

### prasanna

Hi!
Here's one problem.
A piece of iron(with cavities) weighs 6000 N in air AND 4000 N in water.The density of iron is 7.87 g/cc.What is the volume of cavities?
My assumption is that the weight of water displaced is equal to the buoyant force(which is right because Archimedes said so). The problem is what volume of water is displaced? Is it right to say that the volume of the iron piece without the cavities is the volume of water displaced? :uhh:

2. Feb 9, 2005

### Andrew Mason

The volume of the iron (ie. just the iron, without the cavities) is the mass/density (density = 7.87e3 kg/m^3). The mass is the weight (mg) divided by g. The buoyant force is equal to the weight of the water displaced. The volume of water displaced is equal to the volume of the iron and cavities (assuming the cavities are watertight).

Therefore the mass of the iron is 6000/9.8 = 612.25 kg
The volume of just the iron, therefore, is: 612.25/7.87e3 = .07780 m^3
2000 N of water = 2000/9.8 = 204 kg = .204 m^3 = volume of water displaced.

So, what is the volume of the cavities?

AM