Infusoria and the red tide
[For purposes of this problem, assume each individual infusorium is a cube with a side length of exactly 12/1000 of an inch, and they are packed together in a cubical lattice.]
A red tide in the Gulf of Colzoum was caused by the presence of a massive collection of infusoria, all of which are red in color.
The layer of infusoria is exactly 6 inches thick and has a surface area of precisely 50 square nautical miles. How many infusoria are present in the red tide?
Details: 1 nautical mile = 6,000 feet
The answer is 900000000000000000.
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1 solution
The thickness of the layer is precisely 500 infusoria. There are (1000/12 * 12) = 1000 infusoria per foot, so each square foot of surface has 1,000,000 of them per layer = 500.000,000 total. There are 36,000,000 square feet in a square nautical mile, so the total number of infusoria is 500.000,000 * 36,000,000 * 50 = 900,000,000,000,000,000