The Great Pyramid of Cheops is a right square pyramid
with height of 148 m and a square base with a perimeter
of 940 m. The Transamerica Building in San Francisco
has the basic shape of a right square pyramid that has a
square base with a perimeter of 140 m and a height of
260 m. Which one has the greater volume and by how
many times as great?
Volume = (1/3)*(P/4)^2*H = (1/48)P^2*H
where P is the perimeter and H is the height.
V(Cheops)/V(Transamerica)
= (148/260)*(940/140)^2
= 25.7
Well, the Great Pyramid of Cheops and the Transamerica Building seem to be competing in the pyramid Olympics! Now, let's calculate their volumes to see who takes home the gold.
To find the volume of a pyramid, we use the formula V = (1/3) × base area × height.
Let's start with the Great Pyramid of Cheops. As it has a square base with a perimeter of 940 m, we can easily calculate its base side length. Dividing 940 m by 4 (since the perimeter of a square is 4 times its side length), we have a base side length of 235 m. So, the base area of the pyramid is 235 m × 235 m = 55,225 m².
The height of the Great Pyramid is 148 m. Now, we can calculate its volume using the formula: V = (1/3) × 55,225 m² × 148 m = 2,583,038.67 m³.
Now, let's take a trip to San Francisco and check out the Transamerica Building. Its square base has a perimeter of 140 m, so the side length of its base is 140 m ÷ 4 = 35 m. The base area is then 35 m × 35 m = 1225 m².
The height of the Transamerica Building is 260 m. Using the formula, V = (1/3) × 1225 m² × 260 m = 107,166.67 m³.
Comparing the volumes, we find that the Great Pyramid of Cheops has a volume of 2,583,038.67 m³, while the Transamerica Building clocks in at 107,166.67 m³.
So, the Great Pyramid of Cheops has a volume about 24.09 times greater than the Transamerica Building! That's quite a towering difference!
To compare the volumes of the Great Pyramid of Cheops and the Transamerica Building, we can use the following formula for the volume of a right square pyramid:
Volume = (1/3) * base area * height
Let's calculate the volumes of both pyramids:
1. Great Pyramid of Cheops:
Since the base has a perimeter of 940 m, and it is a square, the length of each side of the base can be found by dividing the perimeter by 4.
Side length of the base = 940 m / 4 = 235 m
The base area is the square of the side length:
Base area = (235 m)^2 = 55225 m^2
Height = 148 m
Volume = (1/3) * (55225 m^2) * 148 m
Volume ≈ 2,439,629 m^3
2. Transamerica Building:
Since the base has a perimeter of 140 m, and it is a square, the length of each side of the base can be found by dividing the perimeter by 4.
Side length of the base = 140 m / 4 = 35 m
The base area is the square of the side length:
Base area = (35 m)^2 = 1225 m^2
Height = 260 m
Volume = (1/3) * (1225 m^2) * 260 m
Volume ≈ 106,667 m^3
Therefore, the Great Pyramid of Cheops has a greater volume than the Transamerica Building by approximately 22.88 times.
To find the volume of a pyramid, we use the formula:
Volume = (1/3) * base area * height
Let's first find the base area and height for each pyramid.
For the Great Pyramid of Cheops:
The square base has a perimeter of 940 m, which means each side has a length of 940 m / 4 = 235 m.
The height is given as 148 m.
For the Transamerica Building:
The square base has a perimeter of 140 m, which means each side has a length of 140 m / 4 = 35 m.
The height is given as 260 m.
Now, let's calculate the volume for each pyramid.
For the Great Pyramid of Cheops:
The base area is the length of one side squared, so it is 235 m * 235 m = 55225 m^2.
Using the volume formula, we have:
Volume = (1/3) * 55225 m^2 * 148 m = 1311566.67 m^3
For the Transamerica Building:
The base area is the length of one side squared, so it is 35 m * 35 m = 1225 m^2.
Using the volume formula, we have:
Volume = (1/3) * 1225 m^2 * 260 m = 1066666.67 m^3
Comparing the volumes:
1311566.67 m^3 (Great Pyramid of Cheops) > 1066666.67 m^3 (Transamerica Building)
The Great Pyramid of Cheops has a larger volume by approximately 246900 m^3.