How big is a million dollars? At one point in time, the price of gold was about

Question

How big is a million dollars? 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/cm^3 and that of silver is 10.5 g/cm^3. If you found a spherical gold nugget worth $2 million, what would be its diameter? Express your answer in centimeters to three significant figures. How much would a silver nugget of that size be worth? Express your answer in dollars to two significant figures.

Explanation / Answer

Part A:

price of gold per ounce=$1400

price of silver per ounce=$20

1 troy ounce=31.1035 g

price of gold per gram=$1400/31.1035g= $45.011/g

price of silver per gram=$20/31.1035g= $0.643/g

Part A:

Mass of gold in $ 2million=44433.583 g

Volume of gold=44433.583/19.3=2302.258 cm3

For spherical nugget =(4/3)pi*r3=2302.258 cm3

   r= 8.174 cm

So diameter of gold nugget=16.348 cm

Part B:

Now radius of silver nugget=r=8.174 cm

Then Volume=2287.665 cm3

Then Mass of silver nugget=2287.665 * 10.5=24020.4825 g

As price of silver per gram=$20/31.1035g= $0.643/g

Then the worth of this silver nugget= $15445.170

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