# math

according to the smithsonian institute, many of the original stones were removed and or eroded. The length of one side of the square base originally measured 207 ft. less than twice the height. The original volume of the great pyramid was 91,394,008 ft.cubed. Use the formula for the volume of a square pyramid to calculate the original base and original height of the great pyramid...
the formula is Vsquare pyramid=1/3L^2H

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1. L = 2h - 207
so
L^2 = (4 h^2 - 828 h + 42849)

(1/3) L^2 h = 91,394,008
(1/3)(4 h^3 - 828 h^2 + 42,849 h )= 91,394,008

4 h^3 - 828 h^2 + 42,849 h - 274,182,024 =0
try h = 450
364,500,000 - 167,670,000 + 19,282,050-274,182,024 =-58,069,974
try h = 475
428,687,500 - 186,817,500 + 20,353,275 -274,182,024 = -11,958,749
try h = 480
442,368,000 - 190,771,200 + 20,567,520 - 274,182,024 = -2,017,704
graph these and look for where it hits zero, probably around 481 ft

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