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?

Transcribed Image Text:

a V =-h(a² + ab + b²), 3