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### Finding the Surface Area of Rocks

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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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Associated Topics:
College Higher-Dimensional Geometry

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