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Assuming a radius of 50 nanometers (at the center of the estimated range) of Sars-CoV-2, the volume of a single spherical viral particle is equivalent to 523,000 cubic nanometers.
Multiplying this very small volume by the very large number of particles that we calculated earlier, and converting them to meaningful units, we get a total volume of about 120 milliliters. If we wanted to collect all of these virus particles in one place, we have to remember that the spheres do not come together perfectly.
If you think about the pyramid of oranges that you might see in the grocery store, you’ll remember that a significant portion of the space it takes up is empty. In fact, the best you can do to minimize void space is a configuration called “closed sphere wrapping” in which the void space takes up about 26% of the total volume. This increases the total collected volume of Sars-CoV-2 particles to about 160 milliliters – easily small enough to fit in about six shot glasses. Even taking the higher end of the diameter estimate and factoring in the size of the spike proteins, not all Sars-CoV-2 would still fill a can of soda.
It turns out that the total volume of Sars-CoV-2 was between my wife’s rough estimate for the teaspoon and the pool. It’s amazing to think that all of the problems, disruptions, hardships and loss of life that have resulted over the past year could be just a few bites of what would arguably be the worst drink in the world. history.
Christian Yates is a lecturer in mathematical biology at the University of Bath and author of The Maths of Life and Death.
This article is adapted from a part which originally appeared on The Conversation, and is republished under a Creative Commons license.
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