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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?
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(a) To answer question (a), find the volume of the pyramid
V = = = 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 = = = 2.99953E+12 joules. (1)
It is the ANSWER 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 ANSWER to question (b).
Solved.
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To read more about this construction. read this Wikipedia article
https://en.wikipedia.org/wiki/Great_Pyramid_of_Giza