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1. 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 man-made structure in the world for more than 3800 years.) Assume that the density of the limestone used was about 150 lb/cubic ft. 2x (a) Estimate the total work done in building the pyramid. (Hint: Draw a side view of the pyramid to find a relationship between the height and width at any level of the pyramid.) You should set up an integral for this value, explaining how you set it up, and then integrate by hand, showing each step, and evaluating at the limits using the Fundamental Theorem of Calculus (rather than just using a calculator). (b) If each laborer worked 10 hours a day for 20 years, for 340 days a year, and did 200 ft-lb /hour of work in lifting the limestone blocks into place, about how many laborers were needed to construct the pyramid?

1. 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 man-made structure in the world for more than 3800 years.) Assume that the density of the limestone used was about 150 lb/cubic ft. 2x (a) Estimate the total work done in building the pyramid. (Hint: Draw a side view of the pyramid to find a relationship between the height and width at any level of the pyramid.) You should set up an integral for this value, explaining how you set it up, and then integrate by hand, showing each step, and evaluating at the limits using the Fundamental Theorem of Calculus (rather than just using a calculator). (b) If each laborer worked 10 hours a day for 20 years, for 340 days a year, and did 200 ft-lb /hour of work in lifting the limestone blocks into place, about how many laborers were needed to construct the pyramid?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. 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 man-made structure in the world for more than 3800 years.) Assume that the density of the limestone used was about 150 lb/cubic ft. 2x 2x (a) Estimate the total work done in building the pyramid. (Hint: Draw a side view of the pyramid to find a relationship between the height and width at any level of the pyramid.) You should set up an integral for this value, explaining how you set it up, and then integrate by hand, showing each step, and evaluating at the limits using the Fundamental Theorem of Calculus (rather than just using a calculator). (b) If each laborer worked 10 hours a day for 20 years, for 340 days a year, and did 200 ft-lb /hour of work in lifting the limestone blocks into place, about how many laborers were needed to construct the pyramid?
Transcribed Image Text:1. 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 man-made structure in the world for more than 3800 years.) Assume that the density of the limestone used was about 150 lb/cubic ft. 2x 2x (a) Estimate the total work done in building the pyramid. (Hint: Draw a side view of the pyramid to find a relationship between the height and width at any level of the pyramid.) You should set up an integral for this value, explaining how you set it up, and then integrate by hand, showing each step, and evaluating at the limits using the Fundamental Theorem of Calculus (rather than just using a calculator). (b) If each laborer worked 10 hours a day for 20 years, for 340 days a year, and did 200 ft-lb /hour of work in lifting the limestone blocks into place, about how many laborers were needed to construct the pyramid?
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