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 756 ft and its height when built was 481 ft. (It was the tallest manmade structure in the world for more than 3800 years.) The density of the limestone is about 150 lb/ft3. (a) Estimate the total work done in building the pyramid. (Round your answer to three decimal places.) × 1012 ft-lb (b) If each laborer worked 10 hours a day for 20 years, for 340 days a year, and did 250 ft-lb/h of work in lifting the limestone blocks into place, about how many laborers were needed to construct the pyramid?

The work is calculated by multiplying the weight of material in the pyramid by the height to which it is raised. On average, the material is raised to the height of the centroid of the pyramid, which is 1/4 of its height from the base.

The weight of material is calculated as the product of the volume of the pyramid and the density of the material.

work = (volume) × (density) × (height of centroid)

= (1/3)b²h × (density) × h/4

= (1/3)(756 ft)²(481 ft) × (150 lb/ft³) × (481 ft)/4

= (1/12)(756²)(481²)(150) ft·lb

= 1.6528892562×10¹² ft·lb

work ≈ 1.653×10¹² ft·lb

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Laborers

The work output of each laborer is estimated to be ...

(10 h/day)(340 day/yr)(20 yr)(250 ft·lb/h) = 17,000,000 ft·lb

Then the number of laborers required is ...

# laborers = (total work) / (work per laborer)

# laborers = (1.653×10¹² ft·lb) / (1.7×10⁷ ft·lb/laborer) ≈ 9.723×10⁴ laborers

About 97,230 laborers were needed to construct the pyramid.