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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Can someone help me solving this math calculus II problems?
![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.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbdf55049-8116-4b7e-b52e-092d3ce63c7d%2F410bdf08-c471-4e76-92b7-c2cfc9d6fb1b%2Fo5w79ph_processed.jpeg&w=3840&q=75)
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.]
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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