Assuming a 50 nanometer radius (in the center of the estimated range) of Sars-CoV-2, the volume of a single spherical virus particle turns out to be 523,000 cubic nanometers.
Multiplying this very small volume by the large number of particles we calculated earlier and converting it to significant units gives us a total volume of approximately 120 milliliters. If we wanted to gather all these virus particles in one place, we would have to remember that the spheres do not pack perfectly.
If you think about the pyramid of oranges that you can see in the grocery store, you will remember that a significant part of the space it occupies is empty. In fact, the best you can do to minimize void space is a configuration called “closed sphere packing” in which void space occupies approximately 26% of the total volume. This increases the total collected volume of Sars-CoV-2 particles up to about 160 milliliters, small enough to fit inside about six shot glasses. Even taking the high end of the diameter estimate and taking into account the size of the peak proteins, all Sars-CoV-2s still wouldn’t fill a soda can.
It turns out that the total volume of Sars-CoV-2 was between my wife’s rough estimates for the teaspoon and the pool. It’s amazing to think that all the problems, disruption, hardships, and loss of life that has resulted over the past year could constitute just a few bites of what would undoubtedly be the worst drink ever.
Christian Yates is Senior Lecturer in Mathematical Biology at the University of Bath and the author of The Maths of Life and Death.
This article is adapted from a piece that originally appeared on The Conversation, and republished under a Creative Commons license.
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