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?

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

Fermi Problem is described as:

In physics, particularly in physics education, a Fermi problem, Fermi question, or Fermi estimate is an estimation problem designed to teach dimensional analysis, approximation, and the importance of clearly identifying one’s assumptions. Named for 20th century physicist Enrico Fermi, such problems typically involve making justified guesses about quantities that seem impossible to compute given limited available information.

This is one of the simplest Fermi problems.

Simple Fermi Problem: What is the total length of the thread in a bed sheet?
or
How long of a thread would you need to weave/make a bedsheet?

No, you may not ask “what is the size of the bedsheet?” – look around, make an educated guess about the average size of a bedsheet.

No, you may not ask “what is the thread count of the bedsheet?” – figure out the most common thread count. If you can not figure it out, you can go to the bedroom and guesstimate the length of the thread in a square inch.

Answer is in the comments. Talk Like a Physicist