Physical Science Refer to the formula and the discussion in Exercise 1.(a) Use the express...

Physical Science Refer to the formula and the discussion in Exercise 1.

(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 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.*

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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.)

Exercise 1

Physical Science 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 following figure:

The volume of this pyramid 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 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 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?

*Louisiana Superdome (www.superdome.com).

‡H. A. Freebury, A History of Mathematics. (New York: MacMillan Company, 1968).