Warning – there are many numbers in today’s post. Now you’ll learn more than you ever wanted to know about how the Musing Mind works.
We were joking around in a meeting at my job recently and the question came up, “How many gallons are in the Pacific Ocean?” I can’t remember the exact context, something about creating a questionnaire to confuse everybody in the department. But when I got back to my desk, I couldn’t get the question out of my head. So I spent the next half hour playing with numbers until I could send the following to my pals (including my boss, now he knows how I really spend my day.)
In the following steps, one asterisk signifies multiplication. Two asterisks indicate raising a number to a power. So 1.2*10**3 = 1.2 times ten raised to the third power which is 1,200.
- I start by estimating the Pacific has an average depth of 2 miles (from vague memories of National Geographic specials in my past).
- I figure the Pacific is a rough circle covering slightly less than half the globe (from vague memories of globes I've seen). The circumference of the globe is 24,000 miles (a bit of knowledge I've picked up here and there). So maybe the Pacific is 10,000 miles in diameter . That gives it a radius of 5,000 miles.
- The area of a circle is pi*r squared. Taking pi as 3 (isn't rough estimating fun), that's 3*5,000*5,000 = 3*(5*10**3)*(5*10**3) = 75*10**6 square miles.
- Factoring in the 2 mile depth, that's 150*10**6 cubic miles (150 million cubic miles of water!!)
- There are 5,280 feet in a mile. So a cubic mile is (5*10**3)*(5*10**3)*(5*10**3) = 125*10**9 = 1.25*10**11 cubic feet.
- Multiply that by the Pacific and you get (1.25*10**11) * (150*10**6) = 187*10**17 cubic feet of water.
- The next bit has puzzled me in the past when estimating things. How many gallons in a cubic foot. I cheated and asked Google which promptly told me 7.5. Adding that to the equation makes the Pacific 7.5 * 187 * 10**17 = 1400*10**17 gallons or
I Googled "gallons in the pacific" and one site was here. This site, which I have no reason to trust or distrust, says the Pacific has 170 million cubic miles of water. And it says there are 1.8*10**20 gallons of water. I think that's pretty close to my result, especially considering the number of provisional, vague, and fictitious numbers I used.
(In the interest of full disclosure, the numbers were further off to start with, but I found two arithmetic errors in my calculations and fixed them.)