How many 8cm spheres does it take to fill 1500 gallons?
It does depend somewhat on the shape of the 1500 gallon container.Roughly, though there are 3785.41 cm^3 / gallon.An 8 centimeter diameter sphere has approximate volume 268 cm^3, from 4/3 pi r^3.But a search reveals that “For equal spheres in three dimensions the densest packing uses approximately 74% of the volume. A random packing of equal spheres generally has a density around 64%.”Thus, for random packing, the effective volume of one of the spheres is 268 cm^3 * (1.0 / 0.64). Call this SV for the effective volume of one sphere.Then the number that will fit in the volume is given by:1500 gallons * 3785.41 cm^3 / gallons * (1 sphere / SV cm^3) = number of spheresNote that all the units except “spheres” cancel, giving confidence in the formula.I assume that you can do the arithmetic. Also, the answer should be good to only 2 significant digits.
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