19. A frustum of a pyramid is a pyramid with its top cut off [Figure 23(A)]. Let V be the volume of a frustum of height h whose base is a square of side a and whose top is a square of side b with a > b > 0. (a) Show that if the frustum were continued to a full pyramid, it would have height ha/(a – b) [Figure 23(B)]. (b) Show that the cross section at height x is a square of side (1/h)(a(h – x) + bx). (c) Show that V = }h(a? + ab + b²). A papyrus dating to the year 1850 BCE indicates that Egyptian mathematicians had discovered this formula almost 4000 years ago. (A) (B) FIGURE 23

19. A frustum of a pyramid is a pyramid with its top cut off [Figure 23(A)]. Let V be the volume of a frustum of height h whose base is a square of side a and whose top is a square of side b with a > b > 0. (a) Show that if the frustum were continued to a full pyramid, it would have height ha/(a – b) [Figure 23(B)]. (b) Show that the cross section at height x is a square of side (1/h)(a(h – x) + bx). (c) Show that V = }h(a? + ab + b²). A papyrus dating to the year 1850 BCE indicates that Egyptian mathematicians had discovered this formula almost 4000 years ago. (A) (B) FIGURE 23

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

ChapterA: Appendix

SectionA.2: Geometric Constructions

Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...

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