Assuming a 50 nanometer radius (in the middle of the estimated range) of Sars-CoV-2, the volume of a single spherical virus particle is 523,000 cubic nanometers.
By multiplying this very small volume by the very large particles we calculated earlier, and converting it into significant units, we give a total volume of about 120 milliliters. If we want to put all these virus particles in one place, then we need to remember that spheres do not fit together perfectly.
When you think of the pyramid of oranges you can see in the grocery store, you will remember that much of the space it occupies is empty. In fact, the best you can do to minimize empty space is a configuration called ‘close packaging’ in which empty space is approximately 26% of the total volume. It increases the total collected volume Sars-CoV-2 particles up to about 160 milliliters – easily small enough to fit in about six shot glasses. Even if the Sars-CoV-2 takes the top end of the average estimate and takes into account the size of the vein proteins, it will still not fill a can of soda.
It turns out that the total volume of Sars-CoV-2 was between my wife’s rough estimate of the teaspoon and the pool. It is surprising to think that all the problems, the disruption, the hardship and the loss of life that have resulted in the past year could only make up a few mouthfuls that would undoubtedly be the worst drink in history.
Christian Yates is a senior lecturer in mathematical biology at the University of Bath and the author of The Maths of Life and Death.
This article was adapted from a piece that originally appeared on The Conversation, and is published under a Creative Commons license.
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