Question

1.Each of the sides of the base of the Great Pyramid measures 230.4 meters while the

height (vertical distance from the top) measures 145.5 meters. How close is the ratio of
side length to height to the Golden Ratio?
2. The entire pyramid was originally covered with a layer of white limestone. Calculate the area of the limestone used. 3.Compare the total surface area of the sides to the area of the square base. How does this relate to the Golden Ratio? Calculate the perimeter of the base of the pyramid as well as the circumference of a circle with a radius equal to the height of the pyramid

Answer 1

The ratio of the side length to height of the Great Pyramid is close to the Golden Ratio. The area of the limestone used to cover the pyramid can be calculated by finding the surface area of the pyramid. The ratio of the total surface area of the sides to the area of the base is not related to the Golden Ratio. The perimeter of the base of the pyramid is 921.6 meters and the circumference of a circle with a radius equal to the height of the pyramid is 914.73 meters.

Step-by-step explanation:

The ratio of side length to height of the Great Pyramid is 230.4/145.5 = 1.585. The Golden Ratio is approximately 1.618, so the ratio of side length to height is close to the Golden Ratio.

To calculate the area of the limestone used to cover the entire pyramid, we need to find the surface area of the pyramid. The surface area of the sides can be calculated by multiplying the perimeter of the base by the slant height, and the area of the base is the side length squared. Summing these two areas will give us the total surface area of the pyramid. The perimeter of the base is 4 * 230.4 = 921.6 meters. The slant height can be found using the Pythagorean theorem, which is the square root of (height squared plus half the base squared). The slant height is approximately 254.55 meters. So, the surface area of the sides is 921.6 * 254.55 = 234,433.92 square meters. The area of the base is 230.4 * 230.4 = 53,084.16 square meters. Adding these two areas together, we get a total surface area of 287,518.08 square meters.

The ratio of the total surface area of the sides to the area of the square base can be found by dividing the total surface area by the area of the base. The ratio is 287,518.08/53,084.16 = 5.42. This ratio is not related to the Golden Ratio.

The perimeter of the base of the pyramid can be calculated by multiplying the side length by 4, which is 230.4 * 4 = 921.6 meters. The circumference of a circle with a radius equal to the height of the pyramid can be calculated by multiplying the height by 2π. The circumference is 145.5 * 2 * π = 914.73 meters.