The Great Pryamid of Cheops has a square base of 771ft. on a side and a height of 4186ft. How many rooms 35ft x 20ft x 8ft would be needed to have a volume equivalent to that of the Great Pryamid?
b = area of base
V = (bh)/3
V = (594,441 * 4,186)/3
V = 829,443,342 cubic feet in the pyramid
Divide the total cubic feet by the volume of a room to get the number of rooms
To find the number of rooms needed to have a volume equivalent to that of the Great Pyramid, we need to calculate the volume of both the pyramid and the rooms, and then divide the volume of the pyramid by the volume of a single room.
Let's start by calculating the volume of the Great Pyramid of Cheops:
Volume of a pyramid = (base area × height) / 3
The base area of the pyramid is given as a square with sides of 771ft, so the base area is:
Base area of the pyramid = (771ft) × (771ft) = 594,441ft²
Now, we can calculate the volume of the pyramid:
Volume of the pyramid = (594,441ft² × 4186ft) / 3 ≈ 784,507,464ft³
Next, let's calculate the volume of a single room:
Volume of a room = length × width × height = (35ft) × (20ft) × (8ft) = 5,600ft³
Now, we can find the number of rooms needed:
Number of rooms = Volume of the pyramid / Volume of a single room = 784,507,464ft³ / 5,600ft³ ≈ 140,240 rooms
Therefore, approximately 140,240 rooms with dimensions of 35ft x 20ft x 8ft would be needed to have a volume equivalent to that of the Great Pyramid of Cheops.