At the time this problem was written, the price of gold was about $411 per ounce

Question

At the time this problem was written, the price of gold was about $411 per ounce, while that of platinum was about $884 an ounce. The "ounce" in this case is the troy ounce, which is equal to 31.1035g . (The more familiar avoirdupois ounce is equal to 28.35g .) The density of gold is 19.3g/cm3 and that of platinum is 21.4g/cm3 .

Part A

If you find a spherical gold nugget worth 1.00 million dollars, what would be its diameter?

Part B

How much would a platinum nugget of this size be worth?

Explanation / Answer

mass of gold nugget = 1000000/411*31.1035 = 75677.61557gms

density of gold = 19.30g/cc

so volume = 3921.1133cc

so diameter = 9.7822cm*2 =19.56cm

density of platinum = 21.45g/cc

So mass of Pt nugget of same volume = 21.45*3921.1133 = 84107.88gms

So price = 84107.88/31.1035*884 = 2390450.148 dollars

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