The Great Pyramid of Cheops has a square base of 771 ft on a side and a height of 486 ft. How many rooms 25 ft x 20 ft x 8 ft would be needed to have a volume equivalent to that of the Great Pyramid’s?
Pyramid:
V = (b^2 * h) / 3
V = (594,441 * 486) / 3
V = 96,299,442 sq. ft.
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Room:
V = LWH
V = 25 * 20 * 8
V = 4,000 sq. ft.
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96,299,442 / 4,000 = ?________ rooms
To determine the number of rooms needed to have a volume equivalent to that of the Great Pyramid of Cheops, we first need to find the volume of the pyramid.
The volume of a pyramid can be calculated using the formula:
Volume = (1/3) * base area * height
Given that the base of the pyramid is square with sides measuring 771 ft, we can find the base area as follows:
Base area = side^2 = 771 ft * 771 ft = 594,441 sq ft
Now we can calculate the volume of the pyramid:
Volume = (1/3) * 594,441 sq ft * 486 ft = 96,734,814 cubic ft
Next, we need to determine the volume of each room, which is given as 25 ft * 20 ft * 8 ft:
Room volume = 25 ft * 20 ft * 8 ft = 4,000 cubic ft
Finally, we divide the volume of the pyramid by the volume of each room to find the number of rooms needed:
Number of rooms = 96,734,814 cubic ft / 4,000 cubic ft ≈ 24,184 rooms
Therefore, approximately 24,184 rooms measuring 25 ft x 20 ft x 8 ft would be needed to have a volume equivalent to that of the Great Pyramid of Cheops.
To find the number of rooms needed, we need to calculate the volume of the Great Pyramid and then divide it by the volume of each room.
Step 1: Calculate the volume of the Great Pyramid.
The volume of a pyramid is given by the formula: Volume = (Base Area × Height) / 3.
The base area of the Great Pyramid is equal to the side length squared. So, Base Area = 771 ft × 771 ft.
Using the given height of 486 ft, we can calculate the volume of the Great Pyramid:
Volume = (771 ft × 771 ft × 486 ft) / 3.
Step 2: Calculate the volume of each room.
The volume of a rectangular room is given by the formula: Volume = Length × Width × Height.
Given the dimensions of the room as 25 ft × 20 ft × 8 ft, we can calculate its volume:
Volume = 25 ft × 20 ft × 8 ft.
Step 3: Divide the volume of the Great Pyramid by the volume of each room.
Number of rooms = Volume of Great Pyramid / Volume of each room.
Substituting the values into the formula, we get:
Number of rooms = (771 ft × 771 ft × 486 ft) / 3 / (25 ft × 20 ft × 8 ft).
Simplifying the expression gives us the answer to the question.