goldsilverpro said:
Using metric, I would first convert all to cm
Dia = 1mm = .1cm; circumference = pi X Dia = .31416cm
1000m = 100,000cm
.2um = .0000002m = .00002cm
Therefore, there are .31416 x 100000 x .00002 = .628cm3 of gold
The density of Au is 19.3 g/cm3
Therefore, the weight of Au is .628 X 19.3 = 12.1g
Significant Figures
If you really want to be technically "correct" in your answer, you must know the number of "significant figures" in the numbers used to compute this answer. If you've ever had a college physics or chemistry lab, this was most probably taught in the first session. If you know the whole truth about this, I have included links for a couple of very good articles on this subject.
In general, there are 2 types of significant figures, those in the numbers resulting from a count and those resulting from a measurement. In essence, the only ones that are really significant in your answer are those derived from a measurement. Every measurement contains error and that must be reflected in answer. If you have a count of 113 chickens, you don't have 112.7 or 113.1 chickens. Your answer can have no more significant figures than the number with the least significant figures used to compute your answer.
For example, let's say I want to know the circumference of a steel rod, where the circumference is defined as the diameter multiplied by pi. On my calculator, pi is built in to 10 digits - 3.141592654. I measure the diameter of the rod with a digital micrometer that is, say, accurate to the nearest 1/1000". Let's say the rod measures 1.051". I enter pi on my calculator and multiply it times 1.051. The answer given is 3.301813879. Is this correct? The answer is no. The correct answer is 3.302. This has 4 significant figures (count them), the same number of significant figures that is in the number in the calculation with the lowest amount of significant figures - 1.051. Note that the number 3.302 is 3.3018 rounded off. The number written as 3.302 always means a number somewhere between 3.3016 and 3.3024.
In the wire problem, all 3 factors have different significant figures, mainly due to the tolerances inherent in their manufacture. The one with the biggest tolerance, percentage wise, is the plating thickness. It's not easy to hold plating to an exact thickness. Therefore, the best answer is probably 12g and not 12.3 or 12.1. It might even be 10g (with the 2 rounded off), if the plating thickness in reality has only 1 significant figure.
http://www.chemteam.info/SigFigs/SigFigRules.html
https://www.hccfl.edu/media/43516/sigfigs.pdf