Fermi Questions Marathon

[Angstrom]

Assume that there is one baseball park for every high school (order of magnitude, the various factors about cancel each other out?). There are about 10 million high school students, and a high school serves about 2 thousand, so that makes 5000 baseball parks in the US. Because baseball is American, assume 10000 worldwide. A baseball park is a square of side length 150ft, perhaps, so (30m)^2 = 900 m^2. That makes 9 million square meters. A baseball, having diameter 10 cm, takes up 0.01 m^2 space - so 900 million baseballs, so 1E9.

How many woodchuck jokes are told each day?

[hmcginny]

So around 6.5 billion people in the world (-E10), lets say every person makes two woodchuck jokes a year, so divide that by ~180 days so lets say E7 woodchuck jokes per day. Even if each person made 1 a year it would still be E7.

I think you underestimated the number of baseball fields, most colleges have at least 1 field, there are a few hundred pro or semi-pro fields, and then you factor in all of the parks in the US. I would say there are at least 50,000 fields in the US, and thought the rest of the world isn't hugely baseball oriented, but most countries have little league teams. Lets say E5 fields in the world. I agree with your baseball size. and baseball fields are 90 degree sectors of about 300 feet radius or 100m circles, so each set of 4 is 3E4 square meters so E9 square meters total and E11 with the .01 m^2 baseballs.

If the entire U.S. were covered in an inch of rain, how many toilets could be flushed using that water?

[Angstrom]

A toilet is either 5 gallons (1 L) or 1 gallon (5 L) - can't remember which. But liters are usually smaller than I think they are, so let's go with 5 L.

The US is 3000 miles by 1000 miles is 3E6 mi^2 is 12E6 km^2 = 12E12 m^2. An inch is 0.025m = 0.01 m / 4, so we have 3E10 m^3. (3E10 / 5E-3) = 1E13.

The actual answer is more like E5 to E3, because the water couldn't be collected and the vast-vast majority of toilets wouldn't use dirty water. I know that's kind of tongue-in-cheek, but it illustrates a grievance I have with a lot of Fermi questions - there are so many nice ways of asking about real (if obscure and strange) quantities, why should we resort to fantasy scenarios or what basically amounts to the comparison/division/multiplication of two completely unrelated numbers? It practically forces the way you do the problem. I would prefer something more real and direct (though you totally don't have to avoid convolutedness ), such as:

How many carbon atoms are in a hole two feet wide, two feet long, and two feet deep?

[hmcginny]

So there are two ways to view your question: the hole is either filled with air or carbon atoms. I assume you mean carbon atoms. So carbon probably has a density around E1 g/cm^3. 8 ft^3 there are ~3 ft in a meter so around 1/3 m^3 which is 3E5 cm^3. 3E5 * 1E1 = 3E6 g of carbon. Carbon has a molar mass of 12 so there are E6 moles of carbon and thus E29 atoms.

If all of the water on earth was taken and made into a sphere, what would be the surface area of that sphere?

[Angstrom]

The oceans are 10km deep and cover half the Earth, which has a radius of 6400 km. 6.28 * (6400 km)^2 = 3E14 m^2, so 2E14 m^2 * 10km = 2E18 m^3. Multiplying by 3pi/4 gives 8E17 or so, cube root to get 1E6 m.

EDIT: Surface area, not radius! Argh. That makes 1E12 m^2 * 4pi = 1E13 m^2. Also I know I slipped up in the math a bit prior, but order of magnitude I think I'm OK.

Sorry if I was unclear; I am specifically against Fermi questions that are of the form "if you created this unreasonable object, what would its properties be" - because there are enough interesting quantities in the world without you adding your own artificial, rather silly ones. The hole was intended to be filled with air.

How many rolls of masking tape are manufactured each day?

[hmcginny]

Not sure if i can even think of any numbers to help me here... I'd guess E8, but that is purely a guess. 9 seems too high, 7 seems possible, 6 seems a little too low.

How many words are written in the paper version of the New York Times each year?

[Angstrom]

Here's how I would attempt my own problem: production = consumption, the average person uses a roll of masking tape each year, 1E9 / 300 = 1E6. Though I admit that I expect most of the use of masking tape is not by average people, making it hard to measure.

Yours: Assume a newspaper has 50 pages, each page has two sections, each section has four columns, each column has 50 lines, each line has 10 words. A newspaper, then, is 100 * 200 * 10 = 2E5 words (that's 20 pictures!), and let's say it has 500,000 subscribers, for 1E11 words a day. Times 365 is 1E13 words.

How many double bonds are there in the human body?

[cngu23]

Here's how I would attempt my own problem: production = consumption, the average person uses a roll of masking tape each year, 1E9 / 300 = 1E6. Though I admit that I expect most of the use of masking tape is not by average people, making it hard to measure.

Yours: Assume a newspaper has 50 pages, each page has two sections, each section has four columns, each column has 50 lines, each line has 10 words. A newspaper, then, is 100 * 200 * 10 = 2E5 words (that's 20 pictures!), and let's say it has 500,000 subscribers, for 1E11 words a day. Times 365 is 1E13 words.

How many double bonds are there in the human body?

So there are idk..... 10E9 cells in the human body
There are 10E9 Molecules in each cell
8/10 of those molecules have a double bond

so there are 8E19 Double bonds in the human body

Question: How many electrons are there in an iPhone?

[hmcginny]

So an iPhone weighs around 100g, an iPhone is primarily... some sort of metal, metals are towards the middle of the periodic table, lets say the average atom in an iPhone has an atomic number around 45, so a molar mass around 100ish just to make it easy, thus 1 mol of atoms, or 6E23 electrons, times 45 electrons per atom so lets call it E25.

How many years will it take for the world's population to hit 1 trillion? (theoretically, we all know that the earth is physically unable to sustain that many people)

[cngu23]

So an iPhone weighs around 100g, an iPhone is primarily... some sort of metal, metals are towards the middle of the periodic table, lets say the average atom in an iPhone has an atomic number around 45, so a molar mass around 100ish just to make it easy, thus 1 mol of atoms, or 6E23 electrons, times 45 electrons per atom so lets call it E25.

How many years will it take for the world's population to hit 1 trillion? (theoretically, we all know that the earth is physically unable to sustain that many people)

The population is currently around 7 billion, I believe, and we are growing at about 1 billion per 20 years, or 0.05 Billion per year. 1 Trillion divided by 0.05 Billion is 20,000 Years or 2E4 Years.

So my question is: What fraction of the United States is covered by Maple Trees?