Finding the Surface Area of Rocks
Date: 10/5/95 at 22:53:37 From: Anonymous Subject: surface area of rocks I realize that I am not in the K-12, but I have seen some questions in the archives from college students. I am attempting to determine the surface area of rocks (8-12 mm diameter) I am using in a bacterial incubation experiment. The closest reference I have found is to calculate the surface area of a sphere and use correction factor to estimate the surface area. Are there any citations I can look up? You have a similar question in the archives ("ellipsoids"), and say that ellipsoids do not have a mathematical solution for surface area. A geology professor mentioned a roundness factor using the orthogonals of the rock. Any references would sure be helpful. Thanks.
Date: 10/6/95 at 2:43:8 From: Doctor Andrew Subject: Re: surface area of rocks This isn't very mathematical, but how about measuring the surface area by dipping the rocks in some colored chemical, plunking them in water and determining "how much" color there is with some spectro-whatever. If you have some reference surface, a ping pong ball whose surface area you know for example, then I would expect the surface area to be linearly proportional to the color difference. If you want to use a sphere with a correction factor, you could use this method to determine the correction factor, and you could use a water displacement to determine test of volume to decide what size sphere to use. Anyway, these are my two cents worth. Maybe some other Dr. Math around here will have a more mathematical solution. Andrew -Doctor Andrew, The Geometry Forum
Date: 10/9/95 at 14:57:35 From: Doctor Jonathan Subject: Re: surface area of rocks The answer to this question depends very much on the "scale" at which you consider the rock. Technically, surface area is completely unrelated to volume. In fact, you can have an object with infinite surface area but finite volume. The surface of a rock is much like that of a coast-line. That is, fractal. Consider then, the analogous problem of determining the total length of the coast of Hawaii. You could measure it by driving around the shore until you came back to where you started, or you could measure it inch by inch along the beach. However, the latter would give you a much bigger answer than the former, because you would take into account small land features that you would miss when driving. Likewise, you would get an even bigger number if you were to measure the coast-line molecule by molecule. Since you're concerned with bacteria, you're probably only concerned with the surface area of the rock insofar as bacteria can populate it. In this case, the best way to determine the surface area is to find it empirically. If you have a way to coat the rocks in a uniform and known thickness of algar, then you could use the extra weight to calculate the approximate surface area of the rock as "seen" by the bacteria. -Doctor Jonathan, The Geometry Forum
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