31. The Great Pyramid at Giza in Egypt is a square pyramid that measures approximately 756 feet on each side. The height of the pyramid is approximately 450 feet. What is the approximate volume, in cubic feet, of the pyramid?
Answer: B
The approximate volume of the Great Pyramid at Giza is 85,730,400 cubic feet.
To calculate the volume of a pyramid, the formula used is V = (1/3) × base area × height. For the Great Pyramid, the base area is 756 feet × 756 feet, and the height is approximately 450 feet, leading to a calculated volume of approximately 85,730,400 cubic feet.
A) 51,030,000
This option is incorrect as it underestimates the volume of the pyramid. Using the volume formula, even with rounded dimensions, the calculation significantly exceeds this figure, indicating that the base area and height used in this option are not sufficient for the Great Pyramid.
B) 85,730,400
This is the correct answer. The volume calculation using the formula V = (1/3) × (756 × 756) × 450 results in approximately 85,730,400 cubic feet, accurately reflecting the pyramid's dimensions.
C) 226,800
This option is incorrect because it significantly underestimates the volume. The volume of the Great Pyramid, given its large base and height, far exceeds this figure, demonstrating that the calculations leading to this option do not account for the correct dimensions.
D) 453,600
This choice is also incorrect as it is a gross underestimate of the volume. Similar to option C, the calculations for this option fail to consider the large base area and height of the pyramid, which are essential for an accurate volume assessment.
Conclusion
The correct answer, 85,730,400 cubic feet, is derived from applying the volume formula accurately to the dimensions of the Great Pyramid. All other options fail to provide a reasonable approximation, either by underestimating the height or base area, demonstrating that they do not align with the mathematical principles needed to determine the volume of such a large structure.