Assuming a radius of 50 nanometers (in the center of the estimated range) of Sars-CoV-2, the volume of a total spherical virus particle will be 523,000 cubic nanometers.
Multiplying this very small volume by the very large number of particles we have calculated above and converting it into significant units gives us a total volume of about 120 milliliters. If we wanted to bind all these virus particles in one place, we would have to remember that the spheres do not bind perfectly.
If you think about the pyramid of oranges you can see in the grocery store, you’ll remember that a significant portion of the space it occupies is empty. In fact, the best thing you can do to minimize empty space is a configuration called “sphere packing closure” in which the empty space occupies approximately 26% of the total volume. This increases the total volume collected of Sars-CoV-2 particles up to about 160 milliliters, easily small enough to fit in about six glasses. Even taking the upper end of the diameter estimate and considering the size of the tip proteins, all Sars-CoV-2s would still not fill a can of soda.
It turns out that the total volume of Sars-CoV-2 was between my wife’s approximate approximations on the teaspoon and the pool. It’s amazing to think that all the problems, disruptions, hardships, and loss of life that have resulted over the past year could be just a few snippets of what would arguably be the worst drink in history.
Christian Yates is a tenured professor of mathematical biology at the University of Bath and author of The Maths of Life and Death.
This article is adapted from a piece that appeared originally in The Conversation and is republished under a Creative Commons license.
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