Solve the problem.
An amazing formula from ancient mathematics was used by the Egyptians to find the volume of the frustum of a square pyramid, as shown in the figure. 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.
(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 to the nearest thousand feet.
(b) Try to visualize the figure if a = b. What is the resulting shape? Find its volume.
(c) Let a = b in the Egyptian formula and simplify. Are the results the same?
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