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Instructions: Write a clear, complete description of your solution. Neatness counts. Although you may work with other students to check your progress and/or the reasonableness of your answer, copying is prohibited. Cases of copying or suspected copying will be turned over to the Honor Council for investigation. |
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The Great Pyramid of Khufu, near Giza, Egypt, is a right pyramid with a square base. Use 750 ft. as the base length and 480 ft. as the height. (Although these values are not precise, they are quite close and make the numbers work out well.) Find the height f of a frustum such that the frustum’s volume equals half the volume of the Great Pyramid.
Notes: Some students chose to attack this problem with ratios of similar pyramids (think of the volume ratio between a 6-foot-tall Garrett and a "mini-Garrett"). While this is probably the fastest method, most students seemed to be happier computing the actual volume of the Great Pyramid, dividing by 2, and working backward using similar triangles to find the height of the "mini-pyramid." Which method you choose is entirely up to you. Other methods are possible as well.
One method that does not work is to divide half the volume of the Great Pyramid by the area of the Great Pyramid’s base. Although that produces an answer that is fairly close to the true value (certainly better than the unreasonable f = 240 ft. that many people wrote on Tuesday’s test), that method incorrectly assumes that the cross sectional area is constant, i.e., that the pyramid is a prism. Of course, the pyramid tapers as you move upward. |