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 fi nd the volume of the frustum of a square pyramid, as shown in the following fi gure:

The volume of this pyramid is given by (1/3)h • (a2 + ab + b2),

where b is the length of the base, a is the length of the top, and h is the height. (Data from: H. A. Freebury, A History of Mathematics [New York: MacMillan Company, 1968].)

(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 fi gure 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?