Physical Science One of the most amazing formulas in all of ancient mathematics is the for...

Physical Science One of the most amazing formulas in all of ancient mathematics is the formula discovered by the Egyptians to find the volume of the frustum of a square pyramid, as shown in the following figure:

The volume of this pyramid is given by

where b is the length of the base, a is the length of the top, and h is the height.‡

(a) When the Great Pyramid in Egypt was partially completed to a height h of 200 feet, b was 756 feet and a was 314 feet. Calculate its volume at this stage of construction.

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(b) Try to visualize the figure if a = b. What is the resulting shape? Find its volume.

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(c) Let a = b in the Egyptian formula and simplify. Are the results the same?

‡H. A. Freebury, A History of Mathematics. (New York: MacMillan Company, 1968).