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Surface Area and Volume of Pyramids

Surface area and volume of solids with a base and lateral faces that meet at a common vertex.

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Burying a Pharaoh

Credit: Digr
Source: http://commons.wikimedia.org/wiki/File:Pyramid_of_Khufu.jpg
License: CC BY-NC 3.0

5,000 years ago, Egyptian emperors (pharaohs) erected pyramids as tombs. The entrance was covered after their death to stop tomb robbers from stealing the precious objects that were buried with them, which they believed they would use in the next world. The pyramids were huge, and a pharaoh?s tomb was hidden somewhere inside by passageways. The location of the passageways was secret, and once the pharaoh had been buried inside, the passageways were blocked off. Sadly, every pyramid was successfully raided by robbers, hundreds of years later.

Amazing But True

The largest pyramid was built by a pharaoh named Cheops (or Khufu) over a 20-year period ending around 2,560 BCE. The Great Pyramid of Cheops contains three chambers and is the only Egyptian pyramid to have both ascending and descending tunnels.

Credit: Laura Guerin
Source: CK-12 Foundation
License: CC BY-NC 3.0

The volume of the Great Pyramid of Cheops is 3.2 million cubic yards. Each side measures 756 feet, and it was so accurately built that the four sides have an error in length of only 2-and-a-quarter inches. The ratio of the perimeter to the height is \begin{align*}2 \pi\end{align*}, suggesting that the Egyptians of this era had known of the existence of \begin{align*}\pi \end{align*} long before the Greeks.

See for yourself: https://en.wikipedia.org/wiki/Great_Pyramid_of_Giza

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A cubic yard of stone weighs about 2 tons, and one person could move 0.1 ton in one day. How many people did it take to build the Great Pyramid in 20 years, assuming workers got one day off each week?

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Image Attributions

  1. [1]^ Credit: Digr; Source: http://commons.wikimedia.org/wiki/File:Pyramid_of_Khufu.jpg; License: CC BY-NC 3.0
  2. [2]^ Credit: Laura Guerin; Source: CK-12 Foundation; License: CC BY-NC 3.0

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