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1. When a region is being rotated about an axis, how do you tell if you will use the disk or washer method? 2. Let R be the region enclosed by the parabolas r=1-y² and z = y² 1. (a) Sketch the region R. y -2 -1 2 H 4 42 2 I (b) Set up the integral for the volume of the solid obtained by rotating the region R about the line z = 2. [Hint: Sketch the shape of a cross-section.]

1. When a region is being rotated about an axis, how do you tell if you will use the disk or washer method? 2. Let R be the region enclosed by the parabolas r=1-y² and z = y² 1. (a) Sketch the region R. y -2 -1 2 H 4 42 2 I (b) Set up the integral for the volume of the solid obtained by rotating the region R about the line z = 2. [Hint: Sketch the shape of a cross-section.]

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Worksheet 7: Volumes by Slicing Keywords: volume, slicing method, solid of revolution, disk method, washer method 1. When a region is being rotated about an axis, how do you tell if you will use the disk or washer method? 2. Let R be the region enclosed by the parabolas r=1-y² and z = y² -1. (a) Sketch the region R. y -2 -1 2 #H 4 -2 2 (b) Set up the integral for the volume of the solid obtained by rotating the region R about the line z = 2. Hint: Sketch the shape of a cross-section.]
Transcribed Image Text:Worksheet 7: Volumes by Slicing Keywords: volume, slicing method, solid of revolution, disk method, washer method 1. When a region is being rotated about an axis, how do you tell if you will use the disk or washer method? 2. Let R be the region enclosed by the parabolas r=1-y² and z = y² -1. (a) Sketch the region R. y -2 -1 2 #H 4 -2 2 (b) Set up the integral for the volume of the solid obtained by rotating the region R about the line z = 2. Hint: Sketch the shape of a cross-section.]
Math 181 Discussion Worksheels 3. Consider the solid whose base is bounded by the curve y = r² and y = 2-², and whose cross sections through the solid perpendicular to the z-axis are squares. (a) Make a sketch of the region. y -2 -1 2 H 4 -2 2 I (b) Make a sketch of the solid. y + I (c) Set up the integral for the volume of this solid.
Transcribed Image Text:Math 181 Discussion Worksheels 3. Consider the solid whose base is bounded by the curve y = r² and y = 2-², and whose cross sections through the solid perpendicular to the z-axis are squares. (a) Make a sketch of the region. y -2 -1 2 H 4 -2 2 I (b) Make a sketch of the solid. y + I (c) Set up the integral for the volume of this solid.
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