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As of this writing, the population of the world is estimated to be growing by about 1% per year. As our numbers grow, we are slowly but surely converting a fraction of the mass of the earth into people.

It's not in the least plausible
to assume we can devour
the whole earth. With every
kilometer you descend into the earth, the
temperature increases by about 25 C (45^{o} F) and the core of the earth is hotter than the surface of the
sun. Instead, let's
consider the more realistic limitation of converting the upper crust -- the
thin surface layer of the earth where we can live -- instead of the entire
earth. Let's assume we could go about 5 km down from the
surface without it being too ridiculously complicated to use the material.

To estimate the mass of the 5 km shell, covering the earth, it is a good approximation for the volume to just take the area of the surface of the earth and multiply by 5 km to get the volume. You will then need an estimate of the density of the earth to get the mass of the shell. (One way to do this is described in problem GR10.) For simplicity, assume the earth has a uniform density.

Then, estimate
how long it would be, at the current rate of growth before we have converted
this entire 5 km shell into people. (It might
be useful to compare this calculation to *Population
growth:1* and the problem of streptococci.)

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Page last modified February 10, 2008: G31