After learning about the Fermi Problem, I decided to try solving one myself. The problems tend to be extreme and mind-boggling in nature and after searching for a while I found something that seemed more docile. Unlike the number of windows in New York City, surely there is an accurate answer to this question, hence I can cross-check my work afterward.

Before you continue reading more, try solving the problem yourself first. It’s actually quite fun!

First Attempt: Deriving from Earth’s Weight

I knew this would be wrong since the ground has a higher density than water. But I did the math anyway since I was curious about the weight of the Earth.

1. I know that 70% of Earth’s surface is water.
2. Let’s assume that ratio extends to the weight too.
3. I Googled⚠️ the mass of the Earth since I obviously don’t know it. It’s around 5.972 * 10^24 kg. Since we are approximating stuff anyway, let’s just say it’s 6 * 10^24 kg.
4. Using #2, 70% of Earth’s mass = 4.2 * 10^24 kg.
5. 1 liter of water has a mass of 1 kg.
6. Using #5, we reach 4 * 10^24 liters.

This is wrong since the solid part of Earth weighs more than the water. But some of the points above are true: #1, #2, and #5. Let’s see if we can reach a better approximation using another method.

Second Attempt: Measuring the volume of the ocean

For the second attempt, I decided to focus on the surface area. If we can calculate the surface area of water and just multiply it by the average depth, we will have an accurate volume of water.

1. I have no clue about how much is the surface area of Earth. So I Googled ⚠️ it. The radius of Earth is 6400 km.
2. Next, I needed the average depth of the ocean. I am ignoring the rest of the water, such as lakes, rivers, and ponds since they will be negligible compared to oceans. I Googled ⚠️ this too. The average depth is 3.6 km (or 4 km to simplify).
3. For a second, imagine 100% of Earth’s surface is covered with water. We can get the volume using the formula V = 4/3 * pi * (6400^3 – 6396^3). That’s around 1.85 * 10^9 km^3.
4. Only 70% of Earth’s surface is water so we multiply #3 by 0.7 to get 1.29 ^ 10^9 km^3.
5. We need to convert the volume to liter. 1 liter is actually 0.001 m^3. If you convert #4 to liter, that becomes 10^21.

This answer is 1000 times smaller than our first attempt. The real answer is 1.23391 * 10^21, which is close to our estimation!

Conclusion

It’s hard to solve Fermi’s problem if you don’t know some basic information about the domain. In this problem, I think knowing Earth’s radius and the ocean’s average depth was crucial.

Then again, perhaps I could have guessed those basic facts too? I could have used the perimeter formula (2*pi*r) to get a perimeter value and used the speed time formula to see how long it takes a car driving at 60 km/h speed to cross that distance. Wasn’t there a book titled Around the World in 80 Days? I could have used that time to see for what radius it takes 80 days.

This is much more fun than I expected. Next time I will try to avoid Googling for basic facts as much as possible.

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