The Great Pyramid of Giza was constructed as a regular pyramid with a square base. It was built with an approximate volume of 2,592,276 cubic meters and a height of 146.5 meters. What was the length of one side of its base, to the nearest meter?(1) 73(3) 133(2) 77(4) 230
Q. The Great Pyramid of Giza was constructed as a regular pyramid with a square base. It was built with an approximate volume of 2,592,276 cubic meters and a height of 146.5 meters. What was the length of one side of its base, to the nearest meter?(1) 73(3) 133(2) 77(4) 230
Understand the formula: Understand the formula for the volume of a pyramid.The volume V of a pyramid with a square base is given by the formula V=31×base area×height. The base area for a square is side length2.
Given values: Given values for the volume and height.Volume V=2,592,276 cubic metersHeight h=146.5 metersWe need to find the base side length s.
Rearrange formula: Rearrange the volume formula to solve for the base area.Base area = (3×Volume)/Height
Substitute values: Substitute the given values into the rearranged formula.Base area =146.53×2,592,276
Calculate base area: Calculate the base area.Base area = 146.57,776,828Base area ≈53,076.77 square meters
Find side length: Find the side length of the square base.Since the base area is the side length squared, we take the square root of the base area to find the side length.Side length s = Base area
Calculate side length: Calculate the side length.Side length s≈53,076.77Side length s≈230.38 meters
Round side length: Round the side length to the nearest meter.Side length s≈230 meters (to the nearest meter)
More problems from Volume of cubes and rectangular prisms: word problems