2. (Volumes of Solids of Revolution). For each of the following plane regions: (a) obtain a description of the region R bounded by the specified curves as a Type I region of the form I= a, R= (v= S(x), y = 9(z)). (or as the union of several Type I regions, if necessary); (b) sketch the region R; (e) sketch the solid Ss of revolution obtained by revolving the region R about the indicated axis/axes; (d) find the volume of the solid S (please make sure to provide some details here, as shown in the table below); (e) round your result in (d) to five decimal places. v = 72/(36 + ), y = 0, 2 = 0, z = 6, about the z-axis; v = e" Va, y = 0, 2 = In(6), about the a-axis; (1) (ii)
2. (Volumes of Solids of Revolution). For each of the following plane regions: (a) obtain a description of the region R bounded by the specified curves as a Type I region of the form I= a, R= (v= S(x), y = 9(z)). (or as the union of several Type I regions, if necessary); (b) sketch the region R; (e) sketch the solid Ss of revolution obtained by revolving the region R about the indicated axis/axes; (d) find the volume of the solid S (please make sure to provide some details here, as shown in the table below); (e) round your result in (d) to five decimal places. v = 72/(36 + ), y = 0, 2 = 0, z = 6, about the z-axis; v = e" Va, y = 0, 2 = In(6), about the a-axis; (1) (ii)
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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Present your answers to the problem in five tables similar to the following table:
Transcribed Image Text:2. (Volumes of Solids of Revolution). For each of the following plane regions:
(a) obtain a description of the region R bounded by the specified curves as a Type I region of the form
I = a,
I= b
R =
y = f(x), y = g(x))
(or as the union of several Type I regions, if necessary);
(b) sketch the region R;
(e) sketch the solid S of revolution obtained by revolving the region R about the indicated axis/axes;
(d) find the volume of the solid S (please make sure to provide some details here, as shown in the table below);
(e) round your result in (d) to five decimal places.
y = 72/(36 +z), y = 0,1 = 0, 1 = 6,
about the z-axis;
y = e"Va, y = 0,2 = In(6),
about the r-axis;
(i)
(ii)
y° = (7 - 2)°, 1 = 0,
about the y-axis;
z/81 + y/36 = 1,1 = 0,
(iv)
about the r- and the y-axis.
(ii)
Transcribed Image Text:Present your answers to the problem in five tables similar to the following table:
Subproblem (•) | Answers
R = the region bounded by the curve
a? + (y – 9)2 = 4 (the closed disk of radius 2
1-axis
centered at the point
I = 2
I = -2,
= 9 - VT- 2, y = 9+ VT- 1
(a)
R =
(b)
Sketch of R
(c)
Sketch of the solid of revolution S (a solid torus)
(d)
vol(S) = *
-2
- 36x VA- 1² dz ='
- 727?.
(e)
vol(S) 710.61152.
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