Hi guys, I just bought a nice little coin for what I think was a bargain but would like to know for sure. Its a coin comprised of both 9ct gold and 22ct gold (see picture below): Heres how I initially worked out the weight of each portion: Total area of coin = 791 mm2 (using radius of 15.875mm) Area of 22ct = 371 mm2 (using radius of 10.875mm) Therefore area of 9 ct = 420mm2 (791-371) I then took these areas as a percentage of total area and multiplied by the total weight of the coin and the purity % to determine the total gold weight of each portion. But, then I realised that the 22ct centre will be heavier than the 9ct ring, so this calculation wouldnt be quite right. Does anyone know how I would determine the actual gold content of the coin? I guess working out the weight per mm2 from say a 22ct gold sovereign and applying that to this coin, wouldnt work due to differing thicknesses? Am very stumped, any help is much appreciated.
erm, given the dimensions how much would the coin weigh if it was all 22k ? you can scale this back until your percentage of 22k = the weight of the coin? this is probably not that accurate though :S you'd need a very precise measurement of the coins volume..
... Also, the density of the 9 carat will vary depending on what the other alloys are. 9 carat with silver will be a different weight as rose gold which has more copper. So can't give you an accurate answer. Could work out a minimum though I guess.
Essentially you have two cyclinders, this might work: :/ Don't know height, lets say its 2mm or 0.02cm Total volume = pi x r squared x h = 3.14 x 2.52015625 sq cm x 0.2 cm =1.583541 cubic cm Volume of centre cylinder = 3.14 x 1.1826562 sq cm x 0.2 cm = 0.742708 cubic cm So vol of outer ring = Total vol - Centre vol = 1.583541 cubic cm - 0.742708 cubic cm =0.840833 cubic cm Density of 24k gold is 19.3grams/cubic cm so Centre = 0.742708 cubic cm x 19.3 grams x 0.916 = 13.130185 grams Outer ring =0.840833 cubic cm x 19.3 grams x 0.375 = 6.085528 grams Total mass = 19.215713 grams Au x $44.60988 = $857.20 That sounds better, anyone want to check? Of course the 2mm height will need to be altered to the exact thickness of the object
What's a decimal point here or there? You have done well ...I never mix maths with mowing.Unless I am counting how long till I have to mow next.Up here in Qld you can see the lawns growing Too much #+*^+# ! rain..the state is awash. Sorry for the off topic burst ... As you were
Mmmm shiney, thanks very much for doing that. Your maths is correct for the volume calculation and yes it is 2mm high. I had no idea that the density calculation existed to convert to a gold weight... so if your assumptions are correct then looks like I got it for a steal (it cost $AUD 610). Although CKs comments suggests that this may not be 100% accurate, but good to get a rough idea. The 9carat portion is white gold, so guess its mixed with nickel. Cheers
No worries, it might not be an accurate total weight, with reference to CK's post, but it would give you an idea of the gold content which is what you were hoping to work out in order to check your purchase price. Good buy bazz1000. You got the nickel for free too! And yes Boyou, it's a touch damp round here, at least I have a lawn to mow and don't need a snorkel and a pair of scissors in order to cut the grass like some other poor folk.
Figures are hard to come by, but the density of 9k is significantly lower, which will mess up your calculations as above. 19.3 * .375 will result in a multiplier that isn't within the above range. Knowing that it is white gold helps though. Is the real equation 12.7 * .375 ? (Use the higher density for white gold) I'd work with the worst case scenario and see what you come up with. I think this is a great puzzle, and look forward to seeing anyone work out a complete solution. I'll look to publish mine when I get back from holidays. Meanwhile check out this site for some more reliable values: http://www.18carat.co.uk/densityofgoldandothermetals.html
Ooops on the previous post, clicked on submit instead of preview. Have now edited. Good info, and also some very good advice from the link above for women I think. "Q: Why am I allergic to some gold jewellery? Of course some men think they are allergic to jewellery, mostly they are just allergic to buying it for their wife because they would rather put the money towards a new BMW, Jag, Ferrari, or such other toy." Now just waiting for someone to crunch the numbers to find the answer to the maths problem.
