Assuming a radius of 50 nanometers (at the center of the estimated range) of Sars-CoV-2, the volume of a simple spherical virus particle is 523,000 cubic nanometers.
Multiplying this very small volume with the very large number of particles we calculated earlier and transforming it into significant units gives us a total volume of about 120 milliliters. If we want to put all these virus particles in one place, then we should remember that the spheres do not pack perfectly.
If you think about the orange pyramid that you could see at the grocery store, you will remember that a significant part of the space it occupies is empty. In fact, the best thing you can do to minimize empty space is a configuration called “closing the packing sphere” in which the empty space takes up about 26% of the total volume. This increases the total volume collected of Sars-CoV-2 particles up to about 160 milliliters – slightly small enough to fit inside six shot glasses. Even if we take the upper end of the estimated diameter and consider the size of the spike proteins, all Sars-CoV-2 would still not fill a can of soda.
It seems that the total volume of Sars-CoV-2 was between my wife’s rough estimates of the teaspoon and the pool. It is amazing to think that all the troubles, troubles, hardships and loss of life that have resulted in the last year could be just a few mouthfuls of what would undoubtedly be the worst drink in history.
Christian Yates is a senior lecturer in mathematical biology at the University of Bath and author of The Maths of Life and Death.
This article is adapted from a piece that initially appeared on Conversation and is republished under a Creative Commons license.
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