Fermi Problems

I thought this will be my first post just because of one reason...................... THIS GUY IS AWESOME!!!!!!

I mean, he is like one of the golden nuggets, one of the rare assets Science could have. Fermi problems give us a glimpse on how brilliant this person was.

Fermi sitting on a chair, using a piece of paper, a pencil , and his brain could calculate stuff like the circumference of the Earth,  what is the weight of the air above lake superior, how many hair are their on a human head, how many molecules are there in a standard classroom, how many piano tumers are there in Chicago and............

*deep breath*                                                                                                                                       How many atoms of your great^n-grandfather who lived about 2000 years ago do you ingest with each meal ............... wait WHAT!!!!!! O_O                                                                                                                                                                                                                                                                                          
yup, thats the wonder of approximations. Lets dive into some of them..........

Q How many Jelly Beans fit in a one Liter Jar?

First, what will the size of a normal bean be? 

We can think of a jelly bean as a small cylinder, 2 cm long and 1.5 cm  long

If we fill the whole bottle with jelly beans. the complete jar wont be filled, and there will be some air spaces left. So we can assume that about 80% of the bottle is filled.

what is the volume of a single Jelly Bean?

Volume of 1 Jelly Bean = h(pi)(d/2)^2  where h=2cm is the height of the cylinder and d=1.5 is the diameter

thus volume= = 2cm * 3.14* (1.5cm/2)^2 = 3.53 cubic cm

The number of jellybeans in a one liter jar is Volume of the Jar/Volume of one bean

= ((8/10) x 1000 cubic centimeters)/(3.53 cubic cm)= 227 jelly beans

Voila! you can check this too! the answer may not be exact, but it will be very near to this!

Q How many piano tuners are there in Chicago???

The question seems very absurd at first and impossible to answer, but hey.............there is a solution to everything!!!

Each individual may not own pianos for their own. A Piano is like a family property, a family will have one piano.

Lets take the number of families in Chicago to be 2,000,000. (its crowded out there)

Of course, every family will not have a piano. we can assume that one out of 5 families have a piano.

Thus the number of pianos is  400,000

Suppose a piano tuner can tune 5 pianos a day, and supposing the number of working days is 200, he can tune 1000 pianos a year.

Frankly speaking, i dont know how much time it takes, till a piano needs tuning. I assume it to be five year.

So in one year, 400,000/5= 80,000 pianos need tuning.

Thus the number of piano tuners is 50,000/1000= 80 piano tuners in the city.

Q How many kernels of popcorn will it take to fill a classroom?

WE can assume that in a cubic inch, there will be nearly 4 popcorn kernels.

 There are 12*12*12 inch cubes in a cubic foot. This value is near 1500. Thus there are 1500*4= 6000 kernels in a cubic foot..

A standard classroom can be taken as 70 feet long and 40 feet wide and nearly 10 feet high.

So the volume of the classroom will be  28000 cubic foot.

Thus the number of kernels in a standard classroom is

28000*6000= 168,000,000.  Phew! thats a LOT!

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You might be thinking that they answers may be waaaay off the actual value as we are taking  huge approximations.

Even though the approximations seem random, the answer is near to the actual values.

The approximation will be of the same order of magnitude as that of the actual answer.

so why does this happen??

in simple words, the errors tend to cancel each other.

The over approximations and the under approximations cancel each other, thus the answer tends to be near the actual value.

During a testing of the nuclear bomb, Fermi was sitting in a lab, near to the bomb site.

When the bomb exploded, he started dropping small pieces of paper to the ground.

When the shock-wave arrived, the small pieces got displaced.

Then on the back of an envelope, he calculated the strength of the bomb to be 10 kilo tonnes, which is quite close to the actual value!!!!!

Thats how  brilliant this method was!!!!!!!!