Final answer:
The total surface area of the Great Pyramid of Cheops, including its base, is 139298.88 square meters. Approximately 20822 stone blocks are estimated to make up the outside facing of the pyramid.
Step-by-step explanation:
The Great Pyramid of Cheops originally had a height of 147 meters and a square base side length of 230.4 meters. To calculate the surface area of the pyramid, we need to find the area of the base first, which can be done by squaring the length of the base side:
Base area = 230.4m x 230.4m = 53092.16m²
Now, to find the surface area of each triangular side, we can use the formula for the area of a triangle (1/2 base x height), but first we need the slant height of the pyramid. This can be calculated using the Pythagorean theorem, since each side of the pyramid is an isosceles triangle where the base is the side of the square and the legs are formed by the slant height:
Slant height, l = √(147m)² + (115.2m)² = √21609 + 13274.44 = √34883.44 = 186.79m
Triangle area = 1/2 base x slant height = 1/2 x 230.4m x 186.79m = 21551.68m²Since there are four identical triangular sides:
Total surface area for four sides = 4 x 21551.68m² = 86206.72m²
Total surface area of the pyramid, including its base = 53092.16m² + 86206.72m² = 139298.88m²
To estimate the number of stone blocks on the outside facing, we must first find the area of one block:
Block area = 2.3m x 1.8m = 4.14m²
If we divide the total area of the four sides by the area of one block, we get the approximate number of blocks needed:
Number of blocks ≈ 86206.72m² / 4.14m² = 20821.746 blocks
Since we cannot have a fraction of a block, we round up to the nearest whole number, resulting in 20822 blocks required for the facing.