Volume of the Great Pyramid 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 1 V=h(a² + ab + b²), h b a a b where b is the length of the base, a is the length of the top, and h is the height. (Source: Freebury, H. A., A History of Mathematics, Macmillan Company, New York.) (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. R.3 Polynomials 35 (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?
Volume of the Great Pyramid 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 1 V=h(a² + ab + b²), h b a a b where b is the length of the base, a is the length of the top, and h is the height. (Source: Freebury, H. A., A History of Mathematics, Macmillan Company, New York.) (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. R.3 Polynomials 35 (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?
Algebra and Trigonometry (6th Edition)
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Transcribed Image Text:Volume of the Great Pyramid 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
1
V=h(a² + ab + b²),
h
b
a
a
b
where b is the length of the base, a is the length of the top, and h is the height.
(Source: Freebury, H. A., A History of Mathematics, Macmillan Company, New York.)
(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.
R.3 Polynomials 35
(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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