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You hav e learned how to determine the area beneath a curve and now we want to use that knowledge to determine the volume of solids. Many interestin g solids can be created and this lab will help you visualize the metho ds used to determine their volumes. Replay the solids often and please be patient with your computer because the images take some time to lo ad completely." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 13 "Introduction: " }}{PARA 0 "" 0 "" {TEXT -1 561 "Throughout history the determination of the volume of solids has occupied great mathematicians across a va riety of cultures. Some very clever procedures have been developed in \+ order to obtain accurate values. In this lab you will learn calculus a pproaches to creating solids and calculating their volumes. Many of th e volume formulas you have previously learned can be verified by the m ethods found in this lab and you will enjoy \"seeing\" how the limit c oncept is so crucial to calculus and its applications.Once agian, be p atient for the images to load fully. " }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 19 "Objectives Defined:" }}{PARA 257 "" 0 "" {TEXT -1 332 "Th e purpose of this module is to improve your conceptual and computation al understanding of how a solid can be generated through the construct ion of disks and shells. Furthermore, the volumes of various solids wi ll be determined through those two constructions using traditional cal culus approaches. These goals will be achieved by " }}{PARA 257 "" 0 " " {TEXT -1 174 "1. Reviewing the construction of disks/washers by revo lving a representative rectangle. Including the examination of both ax es, the proper notation, and student problem sets." }}{PARA 0 "" 0 "" {TEXT 256 168 "2. Reviewing the construction of shells by revolving a \+ representative rectangle. Including the examination of both axes, the proper notation, and student problem sets." }{TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 23 "3. Additional Examples." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 28 "Time Allocation: 50 minut es." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 51 "Review of Disk/Washer Con struction Method (Obj.1):(" }{TEXT 304 16 "Partly Animated)" }}{PARA 0 "" 0 "" {TEXT -1 190 "As with the Riemann Sum Construction for deter mining the area beneath a curve, we can create the same representative rectangular strip and use it to generate 3-D solids. The function f(x ) = " }{XPPEDIT 18 0 "sqrt(x);" "6#-%%sqrtG6#%\"xG" }{TEXT -1 73 " gra phed on [0,2] shown below includes one such representative rectangle. 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