So, I was trying to come up with a basic question involving volume and regular objects, based on some earlier fun math I did with my friend Ramsey about the amount of pennies it would take to fill our dining hall. This is what came out of that brief brainstorm.
So, let’s start by defining some dimensions. An Olympic swimming pool is just any pool which meets the guidelines for Olympic competition. Also, I am going to use a standard US penny.
An Olympic swimming pool is: 50 meters long, 25 meters wide, and at least two meters deep. Or, in United States Customary Units, 164.042 ft long, 82.021 feet wide, and 6.56168 feet deep.
A US penny is: 19.05 mm in diameter (0.75 inches), about 59.817 mm (2.355 inches) in circumference, and 1.52 mm (0.0598 inches) thick.
Some quick volume calculations:
Pool: 50m × 25m × 2m = 2,500 m³ or 660,430.1 gallons
Penny: 9.525 ² × 1.52mm = 433.23 mm³ or 0.026 inches³
Since these measurements of penny volume aren’t very useful, let’s convert:
433.23 mm³/ 1000 = 0.4332300cm³/1,000,000 = 4.33 e-7 m³ or 0.000000433 m³
0.026 in³ / 1728 = 1.50463e-5 feet³ / 0.133681 =1.12 e-4 gallons or 0.0001125541403 gallons
Now we can work it out. If we just assume that the pennies line up evenly (it’s way easier this way) we can just plug our numbers in.
Volume of the pool / volume of the pennies = approximate number of pennies
2,500 m³/ 0.000000433 m³ = 5,773,672,055.427252 pennies or 5.77 billion pennies
660,430.1 gallons/ 0.0001125541403 gallons = 5,867,665,980.475709 or 5.87 billion pennies
If we wanted the value of the pennies, it’d just be the number of pennies divided by 100. So, $57,736,720.55 or $58,676,659.80 (between $57.7 million and $58.7 million)
Based on prices online, it would cost about $300,000 – $500,000 to build an Olympic swimming pool, and about $58 to $59 million to fill it.
Don’t even get me started on dimes.
tl;dr: about 5.77 billion pennies
*Disclaimer* All math performed is subject to rounding error and poor-quality assumptions (like solid pennies acting like a liquid).