Assume a physical object with arbitrary shape whose dimensions are on the order of 1 meter. How would one measure the surface area of the object?
There may be many reasons for determining the surface area:
- Plating or painting the object
- Determining rate of sublimation
- Determining how strongly it smells
- Determining heat loss
If more detail is needed, then assume the object is a rock or stone.
This question is inspired by a similar controversial question on Physics.SE. In that thread it was clear that those with a mathematical background felt that the question was ill-defined, yet some creative answers were proposed. As this is really an engineering question, I feel that a generalized, better-defined version of the question would be on-topic here. See also the meta thread discussing the merits of asking this similar question on Engineering.SE.