Thursday, May 27, 2010

Measuring the Volume of a Container

My sister was packing for an overseas vacation when she found herself with a small bottle of hand moisturizer. Unfortunately, she was uncertain as to whether the bottle was of a size within the travel limits, which was 100ml. My assistance was sought.

The first and probably the most commonsensical solution I came up with was to compare the size of the bottle with other containers of known capacity, such as my water bottle which has 100ml markings. But this method was unsatisfactory as the precision was poor.

I then suggested to fill the bottle with water, and to then measure the amount of water contained. However, this too was unfeasible, since the container already contained some moisturizer.

Being trained or born with scientific and mathematical thinking, I then came up with a most intelligent approach. First, I observed that the container was almost a perfect cylinder. Thus, using a ruler and the simple volume formula, I was able to calculate that the container was almost certainly a 100ml container.

Basic mathematical knowledge proves to be useful to daily life.

In retrospect, a fourth solution is possible, but this is rooted in more science. We can simply immerse the container in a beaker of water such that it is fully submerged. Then, the volume of the container is simply the amount of water displaced. This solution is clearly generalizable to all shapes of containers, assuming they are watertight.

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