How many paperclips would it take to fill all the African elephants in Africa?

1.  Background Story:

Have you ever wondered how many paper clips could fit into an african elephant? No? Well, that probably means you're normal. But what makes great scientists and mathematicians is not being normal, and wondering about the oddest of things. I was having trouble thinking of a challenging problem, when bam, a paper clip fell on my desk, and it looked like an elephants trunk. This popped a question right into my head. How many paper clips would it take to fill an African elephant. But wait, that's way too easy. How many paper clips would it take fill all the african elephants in Africa?

2.  Ask Yourself This:

What is the volume of a paper clip?

What is the volume of an elephant?

How many elephants are in Africa?

3.  Helpful Hints:

I figured out a jumbo paper clip is 4.7 cm long, 1 cm wide, and .1 cm tall making the volume of the jumbo paper clip .47 cm^3, which is about half a cm^3.

There are about 325,000 elephants in Africa
http://wwf.panda.org/what_we_do/endangered_species/elephants/african_elephants/

Elephant dimensions (about)
Elephants height: 3-4 meters tall
http://www.seaworld.org/animal-info/info-books/elephants/physical-characteristics.htm
http://www.kingdomreproductions.com/African_Elephant.html
Elephants width: 2-3 meters
http://www.kingdomreproductions.com/African_Elephant.html
Elephants length: 3 meters
http://www.kingdomreproductions.com/African_Elephant.html


I figured out a jumbo paper clip is 4.7 cm long, 1 cm wide, and .1 cm tall making the volume of the jumbo paper clip .47 cm^2, which is about half a cm^2. I did this by using a meter stick.


I also figured out an elephant is 3.5 meters high, 3 meters long, and 2.5 meters wide which comes out to be 26.25 meters cubed as an elephants volume if it were a box. It is safe to assume in this box the elephant takes up ⅔ of the space, making an elephants volume about 17 meters cubed.



4.  Construct a Formula:
The volume of the elephant in meters cubed times the amount of space a paper clip takes up in centimeters cubed will tell me how many paper clips will fit in a elephant.


Paper Clips         Meters                Elephants          Paper Clips
----------------    x    ----------------   x   ---------------   =   ----------------
Meter                   Elephant             Africa                 Africa


5.  Messy Math:



17m^3                 1,000,000cm^3              2 paper clips             34,000,000 paper clips
----------        x      ------------------      x      -------------------     =     ---------------------------
1 elephant           1m^3                          1cm^3                         1 elephant

34,000,000 paper clips
34000000
3.4000000
7 places
3.4
3.4 x 10^7 paper clips

3.4 x 10^7 paper clips           325,000 elephant        1,105,000 x 10^7 paper clips         1.105 x 10^13 paper clips
---------------------------   x    -----------------------  x  ------------------------------------  =  ------------------------------
1 elephant                                   1 Africa                 1 Africa (elephants in africa)          1 Africa (elephants in Africa)


6.  Answer:

1.105 x 10^11 paper clips in all the elephants in Africa, which is the same as about 10 times the paper clips the US uses in 1 year.

Paper clips used in the US in 1 year:  http://www.theatlanticwire.com/business/2011/08/americans-buy-11-billion-paper-clips-year/41862/