Question 1202499
.
The Great Pyramid of King Khufu was built of limestone in Egypt over a 20-year time period 
from 2580 bc to 2560 bc. 
Its base is a square with side length 230 m and its height when built was 147 m. 
(It was the tallest man-made structure in the world for more than 3800 years.) 
The density of the limestone is about 2400 kg/m3
(a) Estimate the total work done in building the pyramid.
(b) If each laborer worked 10 hours a day for 20 years, for 340 days a year, 
and did 250 J/h of work in lifting the limestone blocks into place, 
about how many laborers were needed to construct the pyramid?
~~~~~~~~~~~~~~~~~~~~


<pre>
(a)  To answer question (a), find the volume of the pyramid

         V = {{{(1/3)*a^2*h}}} = {{{(1/3)*230^2*170}}} = 2,997,666.667 m^3.


     Then multiply the volume by the density to get the mass of the material

         M = V*d = 2997666.667*2400 = 7,194,400,001 kilograms.


     Then multiply the mass by the gravity acceleration g= 9.81 m/s^2 and by one fourth of the height 
     to get the work done (the center of the gravity of a pyramid is at 1/4 of the height)

         W = {{{M*g*(1/4)*H}}} = {{{7194400001*9.81*(1/4)*170}}} = 2.99953E+12 joules.    (1)


     It is the  <U>ANSWER</U>  to question (a).



(b)  The work done by one laborer per "year" is

         w = 340*10*250 = 850000 joules per laborer per year.    (2)


     To answer question (b), divide the number W = 2.99953E+12 joules of (1) by 20w,
     where w is the number w= 850000 of (2).  You will get

         the number of laborer = 2.99953E+12 : (20*850000) = 176,443  (rounded).


    It is the  <U>ANSWER</U>  to question (b).
</pre>

Solved.


-----------------------


To read more about this construction. read this Wikipedia article

https://en.wikipedia.org/wiki/Great_Pyramid_of_Giza