4) Let R be the region bounded by y = 4 - x² and the x-axis where 0 < x < 2. a) Use the method of disks to find the volume of the solid obtained by rotating R about the y-axis. b) Use the method of cylindrical shells to find the volume of the solid obtained by rotating R about the y-axis.
4) Let R be the region bounded by y = 4 - x² and the x-axis where 0 < x < 2. a) Use the method of disks to find the volume of the solid obtained by rotating R about the y-axis. b) Use the method of cylindrical shells to find the volume of the solid obtained by rotating R about the y-axis.
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
Section9.3: Cylinders And Cones
Problem 43E: A frustum of a cone is the portion of the cone bounded between the circular base and a plane...
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Disk vs Shell Method about the y-axis
Transcribed Image Text:**Problem Statement:**
Let \( R \) be the region bounded by \( y = 4 - x^2 \) and the x-axis where \( 0 \leq x \leq 2 \).
**Questions:**
a) Use the method of disks to find the volume of the solid obtained by rotating \( R \) about the y-axis.
b) Use the method of cylindrical shells to find the volume of the solid obtained by rotating \( R \) about the y-axis.
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