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VOLUME OF A TRUNCATED SQUARE PYRAMID 1. Suppose we know that the volume of a pyramid with square base is a third of the product of the height and the area of the base. We want to derive a formula for the volume of a truncated square pyramid having lower base of side a, upper base of side b, and height h. (a) If we put the top back onto the truncated pyramid so that the restored pyramid ah a-b has height H, use similar triangles to show that Hs %3D (b) Now subtract the small upper pyramid from the large one to derive the formula V =h (a2 + ab + b²) for the volume of the truncated pyramid. H. a (c) Recall the Egyptian recipe:

VOLUME OF A TRUNCATED SQUARE PYRAMID 1. Suppose we know that the volume of a pyramid with square base is a third of the product of the height and the area of the base. We want to derive a formula for the volume of a truncated square pyramid having lower base of side a, upper base of side b, and height h. (a) If we put the top back onto the truncated pyramid so that the restored pyramid ah a-b has height H, use similar triangles to show that Hs %3D (b) Now subtract the small upper pyramid from the large one to derive the formula V =h (a2 + ab + b²) for the volume of the truncated pyramid. H. a (c) Recall the Egyptian recipe:

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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or the volume of the truncated pyramid. -1 H. b. a. a. (c) Recall the Egyptian recipe: "If you are told: A truncated pyramid of 6 for the vertical height by 4 on the base by 2 on the top, you are to square this 4, result 16; you are to double 4, result 8; you are to square 2, result 4; you are to add the 16, the 8, the 4, result 28; you are to take a third of 6, result 2; you are to take 28 twice, result 56. See, it is 56. You will find it right!" Show that the formula in (b) yields the correct volume for this problem.
Transcribed Image Text:or the volume of the truncated pyramid. -1 H. b. a. a. (c) Recall the Egyptian recipe: "If you are told: A truncated pyramid of 6 for the vertical height by 4 on the base by 2 on the top, you are to square this 4, result 16; you are to double 4, result 8; you are to square 2, result 4; you are to add the 16, the 8, the 4, result 28; you are to take a third of 6, result 2; you are to take 28 twice, result 56. See, it is 56. You will find it right!" Show that the formula in (b) yields the correct volume for this problem.
VOLUME OF A TRUNCATED SQUARE PYRAMID 1. Suppose we know that the volume of a pyramid with square base is a third of the product of the height and the area of the base. We want to derive a formula for the volume of a truncated square pyramid having lower base of side a, upper base of side b, and height h. (a) If we put the top back onto the truncated pyramid so that the restored pyramid ah has height H, use similar triangles to show that H a-b* (b) Now subtract the small upper pyramid from the large one to derive the formula V =h (a² + ab + b²) b2) for the volume of the truncated pyramid. 9. 1 H. a. h. a (c) Recall the Egyptian recipe:
Transcribed Image Text:VOLUME OF A TRUNCATED SQUARE PYRAMID 1. Suppose we know that the volume of a pyramid with square base is a third of the product of the height and the area of the base. We want to derive a formula for the volume of a truncated square pyramid having lower base of side a, upper base of side b, and height h. (a) If we put the top back onto the truncated pyramid so that the restored pyramid ah has height H, use similar triangles to show that H a-b* (b) Now subtract the small upper pyramid from the large one to derive the formula V =h (a² + ab + b²) b2) for the volume of the truncated pyramid. 9. 1 H. a. h. a (c) Recall the Egyptian recipe:
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