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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

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 2,592,276 cubic meters and a height of 146146.55 meters. What was the length of one side of its base, to the nearest meter?\newline(11) 7373\newline(33) 133133\newline(22) 7777\newline(44) 230230

Full solution

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 2,592,276 cubic meters and a height of 146146.55 meters. What was the length of one side of its base, to the nearest meter?\newline(11) 7373\newline(33) 133133\newline(22) 7777\newline(44) 230230
  1. Understand the formula: Understand the formula for the volume of a pyramid.\newlineThe volume VV of a pyramid with a square base is given by the formula V=13×base area×heightV = \frac{1}{3} \times \text{base area} \times \text{height}. The base area for a square is side length2\text{side length}^2.
  2. Given values: Given values for the volume and height.\newlineVolume V=2,592,276V = 2,592,276 cubic meters\newlineHeight h=146.5h = 146.5 meters\newlineWe need to find the base side length ss.
  3. Rearrange formula: Rearrange the volume formula to solve for the base area.\newlineBase area = (3×Volume)/Height(3 \times \text{Volume}) / \text{Height}
  4. Substitute values: Substitute the given values into the rearranged formula.\newlineBase area =3×2,592,276146.5= \frac{3 \times 2,592,276}{146.5}
  5. Calculate base area: Calculate the base area.\newlineBase area = 7,776,828146.5\frac{7,776,828}{146.5}\newlineBase area 53,076.77\approx 53,076.77 square meters
  6. Find side length: Find the side length of the square base.\newlineSince the base area is the side length squared, we take the square root of the base area to find the side length.\newlineSide length ss = Base area\sqrt{\text{Base area}}
  7. Calculate side length: Calculate the side length.\newlineSide length ss 53,076.77\approx \sqrt{53,076.77}\newlineSide length ss 230.38\approx 230.38 meters
  8. Round side length: Round the side length to the nearest meter.\newlineSide length ss 230\approx 230 meters (to the nearest meter)

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