Built around 2600 BCE, the Great Pyramid of Giza in Egypt is 485 ft high (due to erosion, its current height is slightly less) and has a square base of side length 755.5 ft. Find the work W needed to build the pyramid if the density of the stone is estimated at 150 lb/ft3. (Round your answer to three decimal places.)

1.69*10^12 J

Step-by-step explanation:

From figure above, using triangle ratio

485/755.5=y/l. Cross multiplying 485l=755.5y Divide via 485) hence l= 755.5y/485

Consider a slice volume Vslice= (755.5y/485)^2∆y; recall density =150lb/ft^3

Force slice = 150*755.5^2.y^2.∆y/485^2

From figure 2 in the attachment work done for elementary sclice

Wslice= 150.755.5^2.y^2.∆y.(485-y)/485^2

= (150*755.5^2*y^2)(485-y)∆y/485

To calculate the total work we integrate from y=0 to y= 485

Ie W=[ integral of 150*755.5^2 *y^2(485-y)dy/485] at y=0 and y= 485

Integrating the above

W= 150*755.5^2/485[485*y^3/3-y^4/4] at y= 0 and y=485

W= 150*755.5^2/485(485*485^3/3-484^4/4)-(485.0^3/3-0^4/4)

Work done 1.69*10^12joules

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