# Floating objects

Question: How do you find the volume of a floating object?

This is quite a problem.

(a) If you mean how can you find the volume of a floating object if you are allowed to remove it from the liquid then it is easy.
1. Remove the object from the liquid
2. Measure its mass
3. Mark the level of the water in the container
4. Put the object in and record the increase in level of the water – this will give you the volume of liquid displaced by the floating object (this of course is NOT the volume of the whole object).
5. Here is the problem – look up the densities of the object and the liquid, I think that you will need both.

Theory:

Upthrust on floating object = weight of liquid displaced = weight of object (it is floating)
So:
density of solid x volume of solid = density of liquid x volume of liquid displaced

Hence you can work out the volume of the solid.

(b) However if you can't remove it from the liquid then you do have a problem. You might view it through the sides of a transparent container an try and estimate the volume that way, Viewing it from two perpendicular directions would give a very rough idea of the volume. If the liquid is opaque then you would have to resort to finding the volume above the liquid surface. Then you would need both liquid and solid densities to calculate the volume below the surface and then the total volume as above.