Superlesson
Project 5-3
Foundations of Algebra and Geometry
Chapter 5, Spatial Relations
Ancient peoples around the world used massive stones to build burial chambers. Some of the most extensively studied of these chambers are in England and in Egypt.
Part B, Prisms and Volume
1. Stonehenge is the most famous of the ancient sites in Great Britain, but there are many other such sites.
a. Find the measurements (ft) and estimated weight of "Lanyon Quoit".
Part D, Making Connections
2. The three Great Pyramids at Giza, Egypt, are named for the Egyptian pharaohs Khufu, Khephren, and Menkaure. They were built more than 4000 years ago.
a. The Pyramid of Khufu has a square base. Sketch the pyramid, showing the length of each side ("the base") and the original height.
b. Find the quotient
. Round to the nearest hundredth. What famous number does this quotient approximate?
c. Most people believe that the above number was not discovered until at least a thousand years after the Great Pyramids were built. A few people, however, argue that the quotient
d. The height of each face of the Khufu pyramid is 612 ft. Find the surface area of the pyramid (including the base).
e. Here's another demonstration of advanced Egyptian mathematics--or perhaps just a coincidence: Find the square root of the area of one face of the Khufu pyramid. What do you notice about the result?
f. Find the volume of the Khufu pyramid.
g. Record data on the weight and number of stones used to build the Khufu pyramid. Use your answer to f to find the volume of each stone and the density of each stone--the weight per cubic foot.