Volume of the Great Pyramid One of the most amazing formulas in all of ancient mathematics...

Volume of the Great Pyramid 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 figure on the next page. Its volume is given by

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

(a) When the Great Pyramid in Egypt was partially completed to a height h of 200 ft, b was 756 ft, and a was 314 ft. 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?