Math CentralQuandaries & Queries


Question from Patrick:

An irregular shaped object (lets say a gold nugget, not smooth with pockets) can have its volume determined by comparing its mass in water.

Is there any method or means or anything that could be used to determine the surface area of this shape? Whether that be theoretical mathematical formula to using a special infrared technique,etc...

The problem I foresee is that the component parts cannot be divided into smaller geometric shapes. I would propose an answer although I don't know if it is a good one: A liquid material that dries super-thin, but has a very specific and easily determined volume/mass is coated over the object. Measure the mass difference between the beginning sample of fluid and the mass after the object has been coated. Then determine the surface area of the same mass of fluid in a geometric shape.
Is this feasible?

I thank you for your time


The idea ia a good one. However, getting a uniform thickness may be hard.

Any solution will have limitations, because many surfaces that appear in nature are fractal and actually do not have a well-defined area (the smaller the scale you look at the more pockets you find and the bigger the area appears) Choosing a "paint" of a given viscosity effectively chooses a scale but the choice is arbitrary.

If you know why you want to measure the "surface area" this may give you a hint how to do it.


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