Archaeology students are constructing a replica of the Great Pyramid of Giza that they will then fill with sand. The replica is to be 120the size of the original pyramid. The Great Pyramid is approximately 147 meters tall and each side of the base is approximately 230 meters long. Based on these measurements, how many cubic meters of sand will the students need? Round your answer to the nearest whole number.
Answer: 972 m^3 of sand
Step-by-step explanation:
Height of original pyramid = 147 meters
Each side of the base = 230 meters (that is both the base length and base width).
If replica pyramid is to be 1/20 the size of the original pyramid :
Size dimension of replica pyramid will therefore be,
Height = 1/20 × 147 = 7.35metres
Each Base = 1/20 × 230 = 11.5 metres
To calculate the amount of sand required, we can get these by Calculating the volume of the pyramid which us the amount of space occupied by an object.
The volume of a pyramid is given by:
(Base length × base width × height) ÷ 3
( 7.35 m × 11.5 m × 11.5 m) / 3
972.0375 m^3
That means the volume of the pyramid is 972.0375 m^3
. You would start by squaring 400, getting 160,000. You would then multiply 160,000 by 3.14, getting 502,400 meters squared as your answer.