# how much space does a billion dollar occupy?

• Jul 22nd 2013, 08:07 PM
mpx86
how much space does a billion dollar occupy?
just curious to know ....(since it can be regarded as a math question)

how much space does a billion dollar occupy?

1.if they are in currency of 100 dollars
2.maybe in some form of other asserts (gold etc.)
• Jul 22nd 2013, 09:06 PM
topsquark
Re: how much space does a billion dollar occupy?
Quote:

Originally Posted by mpx86
just curious to know ....(since it can be regarded as a math question)

how much space does a billion dollar occupy?

1.if they are in currency of 100 dollars
2.maybe in some form of other asserts (gold etc.)

You would need to know the length, width, and thickness of the bills first.

-Dan
• Jul 23rd 2013, 01:44 AM
ChessTal
Re: how much space does a billion dollar occupy?
Quote:

Originally Posted by mpx86
just curious to know ....(since it can be regarded as a math question)

how much space does a billion dollar occupy?

1.if they are in currency of 100 dollars
2.maybe in some form of other asserts (gold etc.)

The one hundred dollar bill of USA has dimensions width x length of about 15.6 cm x 6.6 cm.
If we assume that(i guess it's about right) a pack of 100 100-dollar bills stacked the one above the other(obviously in the area that is defined by its width and length) has 1 cm height then it's easy to find the volume.

Let's call a bundle, a pack of 100 100-dollar bills. One such bundle has 10000 dollars value.
For 10^9 dollars you need 10^9/10^4 = 10^5 such bundles to use.
Since the volume of one bundle is 15.6·6.6/10^6 m^3, the 10^5 bundles will take (10^5)·15.6·6.6/10^6 m^3 =~ 10.3 m^3

So we will need about 10.3 cubic meters of 100 100-dollar bills to use.

If we want to practically stack them in a room we could stack them in q rectangular cuboid shape of 1 meter height and with 1.56 m x 0.66 m size of its base's sides length.
That means we would use to create the base 10·10=100 bundles and also 100 bundles(1 m height /1 cm height of each bundle) to fill every column of these.
So we would have 10000 such bundles in a rectangular cuboid of size 1m x 0.66m x 1.56m

But we have 100000 bundles so we would need 10 of these rectangular cuboids to create a 1 billion dollar stack.
So 1 billion dollars can be stacked into 10 rectangular cuboids of a size 1m x 0.66m x 1.56m