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		A Cement Truck Full of Margaritas...
		This is a class of problem known as a Fermi problem, so named after Enrico Fermi who enjoyed these "back of the envelope" style problems. The Setup (a true story): At a 10K footrace in Austin, Texas (The Capitol 10K to be exact) one of the sponsors brought a cement mixer (truck) full of margaritas. They poured the margaritas into a trough and served them up by scooping cups into the trough, charge: one cash dollar, American. The Questions: What volume of margaritas did they have in the truck? Did they have enough? The answers: The idea of a Fermi problem is to solve it by approximation with the knowledge at hand. So here goes: I know that trucks can't be more than 8 - 8.5 feet wide legally. The hoppers on the backs of the trucks are pear shaped (sort of ) and so it is not straightforward to calculate how much they might hold. I am going to approximate the size of the hopper with a cylinder eight feet in diameter and sixteen feet long. (You might use a sphere or some other simple shape.) The hopper is slanted so it cannot be completely full and the hoppers taper some at the ends so a cylinder might overestimate the volume. I'm going to say that my cylinder can be 60% full to account for the shape and the slant. Ok so the formula for the volume of a cylinder is pir²length. So 3.14x(4^2)80.6 = 2.41 x 10^2 cu ft = 241 cu ft = 8.9 cu yards Ok, so I don't know the conversion factor from cubic feet to gallons so I'm going to have to convert this the hard way, through metric: 241 cu ft 12^3 cu in 2.54^3 cc liter quart gallon ------------------------------------------------------------------------------------------ cu ft cu in 1000 cc 0.946 liter 4 quart The units all cancel so we should be good to go... = 1800 gallons! Is it enough? 1800 gallons is 1800 gal * 128 ounces/gal = 230,000 ounces divided by 12 ounces/drink = 19,200 drinks. Since there were about 10,000 people this is about two drinks per person. However, some were underage and I'm sure that, even in Texas, some were not drinkers. So I'd have guessed that say 40% were one drink, 5% were two drinks and 5% were 3 drinks. By this calculation, (10,000 x .5) + (10000 * .05 * 2) + (10,000 * .05 *3) = 5000 + 1000 + 1500 = 7500 drinks so there should have been plenty. In actual fact, I remember them running out....... Biochemistry 462a Department of Biochemistry and Molecular Biophysics The University of Arizona johno@email.arizona.edu All contents copyright © 1998-2007. All rights reserved. Last revision fall 2007