Physical Science Refer to the formula and the discussion in Exercise.ExercisePhysical Scie...

Physical Science Refer to the formula and the discussion in Exercise.

Exercise

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?

(a) Use the expression (1/3)h(a2 + ab + b2) to determine a formula for the volume of a pyramid with a square base b and height h by letting a = 0.

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(b) The Great Pyramid in Egypt had a square base of length 756 feet and a height of 481 feet. Find the volume of the Great Pyramid. Compare it with the volume of the 273-foot-tall Louisiana Superdome, which has an approximate volume of 125 million cubic feet. (Data from: Louisiana Superdome [www.superdome.com].)

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(c) The Superdome covers an area of 13 acres. How many acres does the Great Pyramid cover? (Hint: 1 acre = 43,560 ft2.)