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Fermi Problem

Christy Tien 85

christy t

on 11 January 2017

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Transcript of Fermi Problem

My Fermi Problem Christy Tien 85 How many hairs are on a head? - How many hairs are in a small unit of area? Estimations The surface area of a hemisphere of radius r is half that of a sphere, Area of hemisphere = 1/2 area of sphere = 1/2 x 4*pi*r = 2*pi*r 2 2 With the radius, r = 1/2 diameter = 5 in and pi equals to approximately 3 , we get Area of "scalp" = 2x3x(5in) = 6x25 in = 150 in 2 2 2 *pi equals to approximately 3 is a close enough approximation to 3.141596... Next I needed some estimate of how many hairs are in a typical patch or unit of area. I counted the number of hairs roughly along a line of 1 inch, somewhere in the middle of my friend's scalp, I counted 40 hairs. Then squaring that, I got 1600 per square inch. 150 in x (1600)in = 240,000 hairs. 2 2 There are about 240,000 hairs on an average person's head. - Whose head is being discussed? - What is the area of an average person's scalp? Sources Thanks for listening! First, to get the area of a scalp, I used a geometric estimate which was my model. I did this because the actual measurement of that area would be really difficult to solve for any head. The model I used is a hemisphere, which has the same diameter as a typical head. The diameter is about 25 centimeters. You can check your own head by looking in the mirror with a ruler across your face. Subordinate Questions http://www.basic-mathematics.com/surface-area-of-a-sphere.html Here are the sources I used to help me answer my question:
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