| Problem # |
Problem |
Solution |
Problem source and
notes |
| 1 |
How many piano tuners in Chicago? | Source: Fermi |
|
| 2 |
How many people
could comfortably stand on a tennis court? (or, if you prefer, a
football field?) Or, consider -- If all the people of the world were crowded together, how much area would we cover? |
Dimensions of tennis
court = 26 yards x 12 yards = 78 ft * 36 ft Dimensions of football field = 120 yards x 53 yards Average dimensions of space taken by person = 1' x 1' = 1 sq foot Thus 78 * 36 = 3000 people could fit onto a tennis court or 120 * 3 * 53 * 3 = 60,000 people could fit onto a football field. 6 billion people, lets assume all crowded up in a square. we need 6 billion sq feet. The edge of this square will be sqrt (6 * 10 ^ 9) = 80000 ft = 27000 m = 27 Km. |
Source: Malcolm
Swan, Univ of Nottingham and Jim Ridgway, Univ of Durham, UK, Plausible
Estimation module. Field-tested Learning Assessment Guide (FLAG). |
| 3 |
How many babies are
born in the USA each minute? |
Population = 300 mil Life expectancy = 75 Assume uniform distribution of people over age # of people 1 yr old = 1/75 * 300 # of babies born per min = 1/70 * 300 * 1/365 * 1/24 * 1/60 mil = 8 per min [US Census website: 1 baby per 8 seconds = 7.5 babies per sec] |
Source: FLAG |
| 4 |
How many K-8 elementary school
teachers are in the USA? |
Given life expectany = 75 and 9
of these years are spent in K-8, the number of kids is approx 1/8 th of
the population. Number of kids in K-8 schools = 300/8 mil Assume for every 25 kids there is a teacher Number of teachers = 300/8 * 1/25 = 1.5 million [1.9 million according to Statistical Abstracts, Hoover Business Press] |
Source: FLAG |
| 5 |
How much is spent on newspapers
in USA? |
300 mil, Assume 3 per household,
100 mil household. Assume each house buys a newspaper a day. Assume it costs 50 cents Per year money spent = 100 * 365 *0.5 mil = 18 billion [26 billion according to SA, HBP] |
Source: FLAG |
| 6 |
How many cars are bought in the
USA? |
300 mil, Assume 3 per household,
100 mil household. Assume 1 car per household Assume a car lives 10 years on an avg So, on an average 1/10th of the cars will be replaced any year = 10 million cars [8 millions in 1997] [133 million cars nationwide in 2000, Stat Abs, 2002] |
Source: FLAG |
| 7 |
How many dentists are there in
US? |
Assume 1 person makes two visits
per year. Assume a dentist sees 10 people a day, or 3650 visits per year Number of visits required per year = 300 mil * 2 Number of dentists = 300 * 2/3650 = 164,000 [160,000 according to SA, HBP] |
Source: FLAG |
| 8 |
How many dump truck loads would it take to cart away Mt. Everest? | Dimensions of Mt. Everest.
Height = 8848 m We can assume it is conical. But I have no idea of what its base dimensions might be. Its definitely steeper than a right circular cone. Couldnt find data on the geometry. |
Source: Science Olympics |
| 9 |
Assuming one Santa Claus visits
all Christian children on Christmas, how fast would he have to travel? And, how many reindeer would he need to pull his sleigh? |
Population of the world 6
billion. 1/3rd christians implies 2 billion christians Given life expectancy of 70, and kids are between 1 and 15, roughly 1/5 th are christian kids. Number of christian kids waiting on Santa = 400 million Assume Santa is spends just a microsecond dropping the gifts for each kid, total time spent in that = 400 s He has now 86000 seconds left to travel. Lets say he will need to make around ten trips round the earth to accomplish this, 240000 miles, roughly 3 miles per second, or 100,000 miles per hour. Pretty fast, and I dont feel like doing reindeers. Too many. |
Source: Science Olympics |
| 10 |
What is the weight of solid garbage thrown away by American families each year? | 100 million households. Averaging 1 to 2 pounds per day? 200 million pounds? |
Source: L. B. Weinstein, Physics
309, ODU |
| 11 |
How much time would be saved nationwide by increasing the speed limit from 55 to 65 mph? How does this compare to the extra lives lost? | 3 people per household, 1 car
per household => 100 million cars. How much is everyone driving? For an average person, 20 miles a day, plus 1000 miles of longer trips => ~ 10,000 miles per year. [Well, SA says about 12000 miles per year on an average vehicle] Total miles driven = 100 billion. Time saved = 100/10 = 10 billion hours 8760 hours in an year, say 10,000 = 1 million years. Well per person, its 10,000/300 = 30 hours. And how do you guess how many more people would accidents happen at this new speed limit? From SA, Total fatalities 41, 821 speeding related |
Source: Weinstein |
| 12 |
If 10% of Californians drive electric vehicles, how many extra power plants will it take to recharge them each night? | Population of California = 35
million Assuming an avg guy drives 20 miles a day? Power consumed by one electric vehicle being driven around by an average californian 10 Kwh, 6-8 hours to charge it. At least 60 Kw for each of these vehicles Total power per day = 60 Kw * 3.5 million An average power plant produces 60 MW of power (per day??) That would mean 3,500 new power plants? More research needed here http://www.eia.doe.gov/cneaf/electricity/ipp/ipp_sum.html |
|
| 13 |
How many individual frames are needed for a feature length motion picture? | 24 frame per second Feature length motion picture = 2 hours? Number of frames = 2 * 3600 * 24 = 18000 frames |
|
| 14 |
What is the heat output of the sun? | Method 1: Non-naive, there must
be something easier - All the energy is being produced by the fusion in the core. - And the energy produced is given by E=mc^2 where m is the mass converted into energy. - 4 protons fuse to form 1 helium nucleus. Mass lost = 0.7% - Mass of hydrogen fusing = 700 mil metric tons per sec - Mass converted into energy = 5 mil metric tons - Find energy by using the formula - what fraction of the energy is heat/light? [Sun produces more energy in 1 sec than humans have in 10,000 years]. [Energy ouptut = 3.83 * 10 ^33 ergs/second, Microsoft Encarta] |
|
| 15 |
How much electrical power does the US use per year? | ||
| 16 |
How much power do humans use? How does this compare to the solar energy incident on the Earth? | ||
| 17 |
How big does a seed on the ground have to be to justify a bird in flying off a tree branch to eat it? (kilograms) | London district science olympics |
|
| 18 |
How many uranium atoms must undergo fission to supply electricity to an average household for one day? (number of uranium atoms) | 1 fission results in 200 Mev =
200 * 10^9 *1.6 * 10^-19 = 3.2 * 10^ -11 J (1 ev = 1.6 * 10 ^-19 J) 1 J = 1/3.2 * 10^11 fissions 1 W = 3 * 10^10 fissions per sec Average power consumption of a house: 10 cents per kWH. Monthly bill of a household = 50 Perday $2 = 20 kWH |
London district science olympics |
| 19 |
If you breath on a window in the winter. a patch of mist will form (1i) the glass. What is the mass of that patch? | Tidal volume = amount of air
that moves in and out per breath ~ 500 ml Inspiratory reserve volume = amount of air that can be inspired forcibly beyond TV ~ 2100 to 3200 ml Expiratory reserve volume = amount of air that can be expired forcibly beyond TV ~ 1000 to 1200 ml Residual volume = amount that remains in lungs after strenuous expiration ~ 1200 ml Amount of water in the exhale ~ 30 ml |
Facts about breathing: 10-15 breaths per min The air flowrate of exhalation is higher than inhalation. Lung volume ~ 3 L Compositions: Atmospheric Air: N2: 78.62, O2: 20.85, CO2: 0.03, H2O: 0.5 Exhaled air: N2: 74.9, O2: 15.3, CO2: 3.6, H2O: 6.2 |
| 20 |
Calculate the number of C02 molecules that are produced from the complete combustion of one litre of gasoline. (number of C02 molecules) | ||
| 21 |
How many kittens were born in the city of London last year? (number of kittens) | ||
| 22 |
How many grains of salt in an average salt shaker? (number of grains) | ||
| 23 |
Estimate how many kilograms of potatoes are eaten each year in North America. (kilograms) | ||
| 24 |
What is the total kinetic energy of all the automobiles in Canada at this moment? (joules) | ||
| 25 |
How many individual hairs does a barber cut. in a lifetime? (number of hairs) | A haircut takes somewhere
between half an hour to an hour. About 10 haircuts a day. Lets say a
barber's career lasts for 30 years. 30 * 10 * 365 ~ 100,000 haircuts Each hai |
|
| 26 |
How many ethanol molecules in a bottle of good Scotch? | 750 ml, 80 proof => 300 ml
ethanol Molecular weight C2 H5 0H = 46g Density of ethanol 0.8 g/ml => 240 g ethanol Number of moles = 6 Number of molecules = 3.6 * 10 ^ 24 |
|
| 27 |
How much warmer is a room when there are ten people in it than when it is empty? | Heat output per person: An average person consumes about 2000 (food) calories per day = 2 * 10^3 * 10^3 calories |
|
| 28 |
How many runs were scored by major league baseball teams during April 2000? | ||
| 29 |
What do you think is the volume of gasoline your car uses in a year? How does this compare to the volume of liquid (water, soda, coffee, etc.) you drink in a year? | Mathematics Assessment Resource
Service (MARS), Univ of Michigan |
|
| 30 |
What is the mass of a fully
loaded Boeing 747? |
QuarkNet, Fermi Labs. |
|
| 31 |
What is the length in miles of
the US Interstate Highway system? |
||
| 32 |
How much tea is there in China? |
1 billion people. 5 cups a day. 5 gms a cup. Lets say they stock an years worth of supply. 25 billion grams = 25 million kilos per day In an year, 365 * 25 ~ 10 billion kilos |
|
| 33 |
Annual cost of healthcare in USA? |
The insurance companies cant be
making a loss, so this gives an upper bound = 300 mil * 1000 = 300 billion. No, there is medicare and other things. |