L> Volume of a Can ( Coke )W. Courtney TrabueEMT-725 Problem SolvingDr. Jim Wilson (Spring 1997)Problem Statement: What is the volume of a 12 ounce can ?Problem Approach:Reading Labels and Volume Conversions for Cooking:Volume can be expressed numerous ways. Using cooking measurements I couldsay a can of 12 fluid ounces is equivalent to one and a half cups. I couldalso buy a can of Coke (12 fluid ounces) and simply read off the side of the can toget the metricmeasure in cubic centimeters ( 355 mL = 355 cu cm ). This is of course anapproximation of the actual volume because the conversion factors used byindustry to lable products alwaysrounds off. Using Technology ( the Calculator )Any advanced calculator will convert volume measurements in fluid ouncesto cubicinches or cubic centimeters automatically. I used my TI-92 calculator toget the equivalent measurement of 12 fluid ounces in terms of cubic centimetersand cubic inches. 12 ounces = 354.88 cubic centimeters = 21.656 cubic inchesThe Old Human Measurement (subject to BIG TIME ERROR)I measured a standard Coke can in the chemistry lab at Georgia MilitaryCollege, Ft. Gordoncampus using a calliper and tape which resulted in the following: height = 4.75 inchesdiameter = 2.6 inchescircumference = 8.1875 inchesBy assuming the can is approximately a "Right Circular Cylinder",I can use the formula I learned in high school algebra for estimating volume:I estimated that the volume was about 25.219 cubic inches.This estimateis "OFF". A Coke can is not "exactly" a Right CircularCylinder. The top and bottom are smaller than the average mid section ofthe can. And, the contents of the can, the liquid Coke, does not fill thecan to the top. (Shaded area represents liquid)I measued the Coke can from the top of the can to the bottom on the firsttrial, and from bottom to top on the second trial. I took the average ofthe two measurements as my hieght. Since the actual contents of the canis somewhat lower than the measured height of the can, my volume estimateis on the high side. This estimate could be imporved were I to measure the actual height of theliquid in the can several times and take the average. Unfortunately, I cannot see through the metal can, so the liquid height can only be estimatedby reducing the can height slightly.I would still have the problem of using an approximate geometric solid (the right circular cylinder) to represent the Coke can. The model does notcompensate for taper at the top and bottom.Extensions:1.
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Extimate the volumes and surface areas of different sizes of containers,not just cylinder types.2. Try to figure out the minimum and maximum surface areas for a given volume.Return to Court"s Home Page