Carefully Researched Solutions

[Ryan Menezes]

Starting this thread to create an archive of Fermi Questions with especially painstakingly researched solutions.

Reading through this archive should be a good way to get a sense of how to approach Fermi Questions.

[Ryan Menezes]

How many grains of rice could fit in all the shoes produced in China last year (2011)?

Let's use the assumptions that (1) shoe production in China is dominated by domestic rather than exports (2) the average Chinese person uses 1 pair of shoes per year (3) we should neglect the fact that space is lost when packing rice into a container.

(5 wide * 12 long * 4 high) (inch^3/shoe) * 2 (shoes/person-year) * (1.5E9 people / China) * 16 cm^3/in^3 ~= 1.2E13 (cm^3 of shoe space / China-year)

I'd approximate the volume of a grain of rice as 1mm x 1mm x 10mm = 1E1 mm^3 = 1E-2 cm^3, so the overall answer would be 1.2E13 / 1E-2 = 15.

Now for the hard/annoying part of Fermi Questions...researching the answer so I'll do better next time:
http://www.unc.edu/~andrewsr/ints092/clark.html says that global shoe production was 10 billion pairs in 1996, and China produced 1/3.
https://www.google.com/search?q=population+of+china says that the population of China is 1.34 billion
http://www.wolframalpha.com/input/?i=grain+of+rice says that the serving volume of a grain of rice is 0.0025 fluid ounces = 0.0739 cm^3
I measured the volume of my own shoe (by stuffing it, then measuring the stuffing). It came out to 43.3 in^3, but I'm a size 8.5

Let's use the assumptions that (1) since 1996 China's share of shoe production has stayed the same, (2) since 1996 global shoe production has grown at the same rate as global population, and (3) my shoe is the average size of shoes produced -- in expectation it is :)

Additional source:
http://www.google.com/publicdata/explore?ds=d5bncppjof8f9_&met_y=sp_pop_totl&tdim=true&dl=en&hl=en&q=world+population
says that world population in 1996 was 5.8 billion, 2011 was 7.0 billion.

Then the "exact" computation (still neglects the fact that space is lost when packing rice into a container) is:
1E10 (pairs/year) * 2 (shoes/pair) * (7.0 / 5.8) * (1/3) * 43.3 (in^3/shoe) * 16.387064 (cm^3/in^3) / (0.0739 cm^3/grain) ~= 7.7E13

It could be a bit bigger since my shoe size may be below average, or a bit smaller because space is lost when packing rice into a container, but overall I'm convinced that it's probably Fermi Answer 14, and almost certainly in the range 13-15.

On Sat, Oct 6, 2012 at 1:56 AM, Ryan Menezes <ry...@fermiquestions.com> wrote:

Starting this thread to create an archive of Fermi Questions with especially painstakingly researched solutions.

Reading through this archive should be a good way to get a sense of how to approach Fermi Questions.

--
current project: http://www.fermiquestions.com