Sep 26, 2008

Posted by in Fermi Friday, Fermi Problems - Simple | 1 Comment

Friday Fermi Problem: How much does a barrel of Gold cost? $1M? $10M? $100M?

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Recently I was listening to the news and the broadcaster was giving numbers on the price of a barrel of oil and and an oz of gold.

Oil is very often referred to as “black gold”, so I started to ponder about the price of a barrel of gold.

You might think that this is a simple multiplication problem, and you are right, it is. But without using a calculator and without searching google, can you do this? Can you come up with an approximate number?

We are just looking for an order of magnitude calculations.

Make a guess, is it $1M, $10M, or $100M?

So with an able 9 year old assistant, who likes to do multiplications, this is what we came up with.

For starters, the broadcaster told us that the gold is at $1,000 per oz.

A barrel is 42 US gallons; but approximate it to 40 gallons.

1 oz is about 31 grams, but approximate it to 30 grams.

The price of gold is given in terms of the weight but the problem asks for the value based on volume, so one needs to do a conversion.

Sigh.. we will have to do this in metric units!

40 gallons is about 150 liters.

Density of gold is about 20 g/cc

So 30 grams of gold is 1.5 cc.

1 liter is 1000 cc

150 liters is 150,000 cc and 1.5 cc of gold costs $1000.

Hence the total cost of a barrel of gold is

(150,000/1.5)* $1000 = 100,000x$1000 = $100M

Really? $100M? that doesn’t sound right. That’s way too high.

Did we miss any zeros?

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Let us double check. How much does a gold bar in Fort Knox cost?

gold bars are about 400 oz. So each gold bar costs about $400k. If you just do a visual comparison, can a barrel accommodate 250 bars?

A typical bar at Fort Knox is 7″x3.5″x1.75″, lets call it 7″x4″x1.5″ approximately.

Barrel is about 30 inches in height and 20 inches in diameter.

So if you try to visualize it, you can put a stack of 20 gold bars and can fit about 10 to 12 of those stacks in a barrel, so it sounds right.

So a barrel of gold costs $100M! Vow.

I know it is right, but I still can’t believe it.

Corollary: If you see a movie of thieves carrying bars of gold, you know that they are faking it. A person can typically carry about 50 -70 lbs. Each bar weighs about 25 lbs. So a person can carry at most 2-3 of the standard size bars. A cubic foot of gold will weigh more than 1000 lbs.

Talk Like a Physicist

  1. A bar of gold at Ft.Knox weighs about 400 oz; so as of today, when the gold prices are $900/oz, a bar of gold costs $360,000.

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