Egyptian Pyramids

Marlys Henke developed the following multicultural activity for her mathematics class:

"PYRAMIDS

Background Information: The Egyptian pyramids were royal tombs for pharaohs. There are about 80 pyramids still standing, and all of them have been broken into and raided for treasures. The Great Pyramid is considered to be one of the Seven Wonders of the Ancient World.

The Great Pyramid is near Cairo, Egypt. It was the first geometrically true pyramid and is the largest. Earlier pyramids were built as a series of steps and had flat tops. The Great Pyramid was ordered built by Pharaoh Khufu (Cheope) about 2600 B.C. At least 100,000 slaves and peasants worked for 20 years to build it. The base is 755 feet by 755 feet and the height was 481 feet. The top 31 feet have been destroyed so the pyramid is only 450 feet high now, with a flat top.

About 2,300,000 limestone blocks were used, each weighing about 2-1/2 tons. The pyramid was built in a series of steps first and then the steps were filled in with white limestone casing stones to make a smooth surface. When the pyramid was finished, it would have appeared to be one gigantic white stone from a distance. Most of the casing stones are now missing, but some remain in place near the base of the pyramid.

Mayan and Aztec Indians of Central and South America also built pyramids. Their pyramids were flat-topped so a temple could be built on the top.

Problem: What was the original volume of the Great Pyramid of Egypt? What is its approximate volume now that the top is missing? Is your approximation too high or too low? Why?"