Cavalieri's Principle states that if a family of parallel planes gives equal cross-sectional areas for two solids S, and S2, then the volumes of S1 and S2 are equal.(a) Does the following proof of Cavalieri's Principle look reasonable?Volume(S1) = ^ A(z)dz = Volume(S2) since the cross-sectional area A(z) at height z is the same for both solids.O yesno(b) Consider the oblique cylinder shown in the figure, with radius of the base r = 2 and height h = 2.hUse Cavalieri's Principle to find the volume V of this oblique cylinder.V =

avalieri's Principle states that if a family of parallel planes gives equal cross-sectional areas for two solids S1 and S2, then the volumes of S1 and S2 are equal. (a) Does the following proof of Cavalieri's Principle look reasonable? Volume(S1) = Soh A(z)dz = Volume(S2) since the cross-sectional area A(z) at height z is the same for both solids. O yes O no (b) Consider the oblique cylinder shown in the figure, with radius of the base r = 2 and height h = 2. h Use Cavalieri's Principle to find the volume V of this oblique cylinder. V=

avalieri's Principle states that if a family of parallel planes gives equal cross-sectional areas for two solids S1 and S2, then the volumes of S1 and S2 are equal. (a) Does the following proof of Cavalieri's Principle look reasonable? Volume(S1) = Soh A(z)dz = Volume(S2) since the cross-sectional area A(z) at height z is the same for both solids. O yes O no (b) Consider the oblique cylinder shown in the figure, with radius of the base r = 2 and height h = 2. h Use Cavalieri's Principle to find the volume V of this oblique cylinder. V=

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.1: Prisms, Area And Volume

Problem 27E: The box with dimensions indicated is to be constructed of materials that cost 1 cent per square inch...

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