document.write( "Question 1202499: The Great Pyramid of King Khufu was built of limestone in
\n" ); document.write( "Egypt over a 20-year time period from 2580 bc to 2560 bc.
\n" ); document.write( "Its base is a square with side length 230 m and its height
\n" ); document.write( "when built was 147 m. (It was the tallest man-made structure
\n" ); document.write( "in the world for more than 3800 years.) The density of
\n" ); document.write( "the limestone is about 2400 kg/m3
\n" ); document.write( "(a) Estimate the total work done in building the pyramid.
\n" ); document.write( "(b) If each laborer worked 10 hours a day for 20 years, for
\n" ); document.write( "340 days a year, and did 250 J/h of work in lifting the
\n" ); document.write( "limestone blocks into place, about how many laborers
\n" ); document.write( "were needed to construct the pyramid? \n" ); document.write( "

Algebra.Com's Answer #837378 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "The Great Pyramid of King Khufu was built of limestone in Egypt over a 20-year time period
\n" ); document.write( "from 2580 bc to 2560 bc.
\n" ); document.write( "Its base is a square with side length 230 m and its height when built was 147 m.
\n" ); document.write( "(It was the tallest man-made structure in the world for more than 3800 years.)
\n" ); document.write( "The density of the limestone is about 2400 kg/m3
\n" ); document.write( "(a) Estimate the total work done in building the pyramid.
\n" ); document.write( "(b) If each laborer worked 10 hours a day for 20 years, for 340 days a year,
\n" ); document.write( "and did 250 J/h of work in lifting the limestone blocks into place,
\n" ); document.write( "about how many laborers were needed to construct the pyramid?
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document.write( "(a)  To answer question (a), find the volume of the pyramid\r\n" );
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document.write( "         V =  =  = 2,997,666.667 m^3.\r\n" );
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document.write( "     Then multiply the volume by the density to get the mass of the material\r\n" );
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document.write( "         M = V*d = 2997666.667*2400 = 7,194,400,001 kilograms.\r\n" );
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document.write( "     Then multiply the mass by the gravity acceleration g= 9.81 m/s^2 and by one fourth of the height \r\n" );
document.write( "     to get the work done (the center of the gravity of a pyramid is at 1/4 of the height)\r\n" );
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document.write( "         W =  =  = 2.99953E+12 joules.    (1)\r\n" );
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document.write( "     It is the  ANSWER  to question (a).\r\n" );
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document.write( "(b)  The work done by one laborer per \"year\" is\r\n" );
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document.write( "         w = 340*10*250 = 850000 joules per laborer per year.    (2)\r\n" );
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document.write( "     To answer question (b), divide the number W = 2.99953E+12 joules of (1) by 20w,\r\n" );
document.write( "     where w is the number w= 850000 of (2).  You will get\r\n" );
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document.write( "         the number of laborer = 2.99953E+12 : (20*850000) = 176,443  (rounded).\r\n" );
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document.write( "    It is the  ANSWER  to question (b).\r\n" );
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\n" ); document.write( "\n" ); document.write( "To read more about this construction. read this Wikipedia article\r
\n" ); document.write( "\n" ); document.write( "https://en.wikipedia.org/wiki/Great_Pyramid_of_Giza\r
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