An Olympic swimming pool is 50.0 meters long by 25.0 meters wide with a depth of 2.0 meters. It has 10 swimming lanes and is used for many Olympic swimming events including the 200m Backstroke, 400m Freestyle, and 100m team relay events. These swimming pools are also used as a unit of measurement. So for our problem today, lets figure out how many 6mm airsoft BBs will fit in an Olympic swimming pool (with the BBs filling the pool and reaching up to the water height level).
What we know:
Pool Dimensions and Volume:
50m x 25m x 2m, 2,500,000 L. (FINA, FR2 Swimming Pools, Federation Internationale De Natation, 2016)
6mm Airsoft BB Dimensions:
5.95mm +/- 0.1 x 5.95mm +/- 0.1
What we don’t know:
How many BBs will it hold?
To find the pool volume:
We can check:
50m x 25m 2m = 2,500m³
Since 1L is equivalent to 0.001m³
2,500 x 1000 liters finds the volume to be 2,500,000 liters
To convert the cubic meters to find our cubic millimeters value:
We convert:
2,500m³ = mm³ / 1000000000
= 2.500000e+12 mm³
2.500000e+12 mm³ = The cubic volume of an Olympic sized swimming pool.
To find the cubic volume of an 6mm spherical airsoft BB:
If a BB is 5.95mm on average for this test, we find:
5.95mm / 2 = 2.975mm for a BB’s radius
The volume of a sphere formula is V = ⁴⁄₃πr³. (Math Open Reference, Volume of a Sphere, 2016)
V = ⁴⁄₃π(2.975)³
V = ⁴⁄₃π(26.330609375)
V = ⁴⁄₃(3.14159)(26.330609375)
V = ⁴⁄₃(3.14159)(26.330609375)
V= 330.879916425625 / 3
V = 110.2933054752083
V = 110.29mm³
110.29mm³ = The cubic volume of a 6mm airsoft BB.
Now, we are almost done. We can apply the concepts of sphere packing here. If we use the best sphere packing ratios to fit as many BBs into the pool as possible, we can use a percentage of 0.7405 (aka π/3√2 for the analytical formula). This is because each spherical BB has gaps between it and the next closest BB it is touching on every side. (Wolfram, Sphere Packing, MathWorld, 2016)
So, 2.500000e+12 mm³ x 0.7405 = How much space we can actually physically fill with our BBs
2.500000e+12 mm³ x 0.7405 = 1,851,250,000,000mm³
Then we can combine the two cubic values:
1,851,250,000,000mm³ / 110.29mm³ = 16,785,293,317.617
So, 16,785,293,317 airsoft BBs is the total amount it would take to fill the Olympic swimming pool.
What did you guess? Please tell us in the comments!
