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ap03_calc_solids_know_23487

# ap03_calc_solids_know_23487 - APCD CALCULUS SOLIDS WITH...

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Solids with Known Cross Sections Page 1 of 2 Copyright © 2003 by College Entrance Examination Board. All rights reserved. Available at apcentral.collegeboard.com APCD CALCULUS: SOLIDS WITH KNOWN CROSS SECTIONS Worksheet to Accompany Exploration, Part 1 Directions: After completing the Exploration, answer the following additional questions. The Exploration is needed to answer some of these questions. 1. For each of the six solids in APCD , “build” the solid [by clicking on the Build button] and then complete the following steps. a) Draw the graph of y x = 1 with a vertical segment at an arbitrary point x to represent the side (or radius) of the cross section. b) Draw a representative cross section. c) Write the general formula for the area of the cross section. d) Write an expression in terms of x for the area of the cross section. e) Write an integral in terms of x for the volume of the solid. f) Verify that your integral is correct by matching the integrals in APCD . g) Find the volume of the solid. 2. Compare the volumes you found for the six solids. Order them from largest to smallest. Which solid has exactly half the volume of another solid? 3. Make a model of one of these solids (out of clay or some other substance, or by building a set of cardboard cross sections). Have you ever seen this type of solid outside of school? Where?

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