At one point in time, the price of gold was about $1400 per ounce, while that of

Question

At one point in time, the price of gold was about $1400 per ounce, while that of silver was about $20 an ounce. The "ounce" in this case is the troy ounce, which is equal to 31.1035 g. (The more familiar avoirdupois ounce is equal to 28.35 g) The density of gold is 19.3 g/cm3 and that of silver is 10.5g/cm3. Part A If you found a spherical gold nugget worth $1 million, what would be its diameter? Express your answer in centimeters to three significant figures. 13.0 cm Submit My Answers Give Up Correct Part B How much would a silver nugget of that size be worth? Express your answer in dollars to two significant figures. Submit My Answers Give Unp ncorrect; Try Again

Explanation / Answer

part(A)

mass of gold m = 10^6/1400 = 714.286 ounces = 714.286*31.1035 = 22216.7946 g

volume = mass/density

volume = 22216.7946/19.3 = 1151.13 cm^3

volume = (4/3)*pi*r^3

r = rdius

1151.13 = (4/3)*pi*r^3

radius = 6.5015 cm

diameter d = 2r = 13.003 cm =13 cm

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volume of silver = volume of gold = 1151.13

mass of silver = density * volume = 10.5*1151.13 = 12086.865 g = 12086.865/31.1035 388.6 ounces

cost of silver$ = 388.6*20 = 7772

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