The Great Pyramid of Cheops has a square base of 771 sq ft. on a side and a height of 486 ft. How many rooms 35 ft.x20ftx8ft would be needed to have a volume equivalent to that of the Great Pyramid?
Vp = Ab*h/3 = 771 * 486 / 3 = 124902F^3
Vr = 35 * 20 * 8 = 5600F^3.
Rooms = 124902 / 5600 = 22.3 or 23.
To calculate the number of rooms needed to have a volume equivalent to that of the Great Pyramid of Cheops, we need to find the volume of the pyramid and divide it by the volume of a single room.
1. Calculate the volume of the pyramid:
Volume = base area x height
The base area is given as 771 sq ft. x 771 sq ft.
The height is given as 486 ft.
Volume = 771 sq ft. x 771 sq ft. x 486 ft.
Volume = 294,343,046 cu ft.
2. Calculate the volume of a single room:
Volume = length x width x height
Given length = 35 ft., width = 20 ft., and height = 8 ft.
Volume = 35 ft. x 20 ft. x 8 ft.
Volume = 5,600 cu ft.
3. Divide the volume of the pyramid by the volume of a single room to find the number of rooms needed:
Number of rooms = Volume of pyramid / Volume of a single room
Number of rooms = 294,343,046 cu ft. / 5,600 cu ft.
Number of rooms ≈ 52,555
Therefore, approximately 52,555 rooms (35 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 out how many rooms with dimensions 35 ft x 20 ft x 8 ft are needed to have a volume equivalent to that of the Great Pyramid of Cheops, we need to calculate the volume of the pyramid first.
The volume of a pyramid is given by the formula:
Volume = (1/3) * Base Area * Height
Given that the Great Pyramid of Cheops has a square base of 771 sq ft on a side and a height of 486 ft, we can calculate its volume as follows:
Base Area = (771 ft)^2 = 594,441 sq ft
Height = 486 ft
Volume = (1/3) * 594,441 sq ft * 486 ft
Volume ≈ 88,478,152 cu ft
Now, let's calculate the volume of one room:
Room Volume = Length * Width * Height
Room Volume = 35 ft * 20 ft * 8 ft
Room Volume = 5,600 cu ft
To find out how many rooms are needed, we can divide the volume of the pyramid by the volume of one room:
Number of Rooms = Pyramid Volume / Room Volume
Number of Rooms ≈ 88,478,152 cu ft / 5,600 cu ft
Number of Rooms ≈ 15,781.456
Since we cannot have a fraction of a room, we would need 15,782 rooms with dimensions 35 ft x 20 ft x 8 ft to have a volume equivalent to that of the Great Pyramid of Cheops.