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
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
To calculate the original base and height of the Great Pyramid, we can use the given information and the formula for the volume of a square pyramid.
Let's first break down the given information:
- 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 is 91,394,008 ft^3.
- The formula for the volume of a square pyramid is Vsquare pyramid = (1/3)L^2H, where L is the length of one side of the base and H is the height.
Now, let's solve the problem step by step:
Step 1: Assign variables to the unknowns.
Let's say the original base length is B, and the original height is H.
Step 2: Convert the given information into equations.
According to the information, we know:
- The length of one side of the base originally measured 207 ft less than twice the height.
This can be written as an equation: B = 2H - 207.
- The original volume of the Great Pyramid is 91,394,008 ft^3.
This can be written as an equation: 91,394,008 = (1/3)(B^2)(H).
Step 3: Substitute the value of B from the first equation into the second equation.
Replace B in the second equation with 2H - 207:
91,394,008 = (1/3)((2H - 207)^2)(H).
Step 4: Simplify the equation and solve for H.
91,394,008 = (1/3)(4H^2 - 828H + 42849)(H)
274,182,024 = 4H^3 - 828H^2 + 42,849H
Now we have a cubic equation, which may require numerical or graphical methods to solve. However, solving this equation without using those methods may not be feasible due to the complexity of the equation.
Therefore, you may need to use numerical methods or graphing software to find the approximate value of H. Once you have the approximate value of H, you can substitute it into the first equation (B = 2H - 207) to find the original base length (B).
Keep in mind that the solution obtained using this method may not perfectly match the exact measurements of the Great Pyramid, as the given values might not be derived from precise historical records.