Question : Built around 2600 BC, the Great Pyramid of Giza in Egypt is 146 m hig

Question

Question : Built around 2600 BC, the Great Pyramid of Giza in Egypt is 146 m high and has a square base of side 230 m . Find the work (against gravity) required to build the pyramid if the density of the stone is estimated at around 2000 kg / m^3 . So far I have done this : Volume of slice = (230 - 230(x)/146))^2 * delta x the mass of the slice = 2000 * (230 - 230x/146 )^2 delta x and Force of the slice is 9.8 * 2000 * (230 - 230x/146 )^2 delta x . The displacement I have is = (146 - x) meters and finally the work equation I have is W = 19600 ( integral of (52900 - (52900*(x)/73) + 13225(x^2)/5329) ) from 0 to 146 + the integral of (146 - x) from 0 to 146 PLEASE FIND MY ERROR somewhere or show me what went wrong.

Explanation / Answer

The mass of each slice is dm = adh, where a = (230-230h/146)2, and the work needed to raise the stone (from ground level) is dw = hdm = h(230-230h/146)2dh, so the work done is:

2000*2302 int(h(1-h/146)2)dh from 0-146

= 2000*2302*int(h - 2h2/146 + h3/1462) from 0-146

=2000*2302*(h2/2 - h3/219 + h4/(4*1462) from h = 0-146

= 2,000*2302*(1462/2 - 1463/219 + 1462/4)

= 1.88 x 10^11 J. (approximate mass-energy of a mosquito egg)

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