can you help answer my question 3. (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 formz= a,I = b(y = f(x), y = g(x))R=(or as the union of several Type I regions, if necessary);(b) sketch the region R;(c) 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.ry = 10, a = 8, r = 9, y = 0,(i)about the r- and about the y-axis;(ii)y = 6 sin z, r = 0, r = n,about the r-axis;y = 8r – r2, y = -r+8,about the r-axis;1? + (y – 8)? = 64,about the r-axis.(iii)(iv)Present your answers to the problem in five tables similar to the following table:Subproblem (*) | AnswersR= the region bounded by the curve1² + (y – 9)² = 4 (the closed disk of radius 2r-axis(C)-centered at the pointx = -2,\y = 9 – V4- a², y = 9+ v4- x² )I = 2(a)R =(Ь)Sketch of R(c)Sketch of S (a torus)*[(19+ va= z²j² - [9 – va – 2² 1* ) dz(d)vol(S) =IVA- z² dx = 72m².= 367(e)vol(S) 710.61152.

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Description: can you help answer my question 3. (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 formz= a,I = b(y = f(x), y = g(x))R=(or a

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Answered: ry = 10, z = 8, x = 9, y = 0, (i) about…

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ry = 10, z = 8, x = 9, y = 0, (i) about the z- and about the y-axis;

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Chapter2: Second-order Linear Odes

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Problem 1RQ

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can you help answer my question

3. (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
z= a,
I = b
(y = f(x), y = g(x))
R=
(or as the union of several Type I regions, if necessary);
(b) sketch the region R;
(c) 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.
ry = 10, a = 8, r = 9, y = 0,
(i)
about the r- and about the y-axis;
(ii)
y = 6 sin z, r = 0, r = n,
about the r-axis;
y = 8r – r2, y = -r+8,
about the r-axis;
1? + (y – 8)? = 64,
about the r-axis.
(iii)
(iv)
Present your answers to the problem in five tables similar to the following table:
Subproblem (*) | Answers
R= the region bounded by the curve
1² + (y – 9)² = 4 (the closed disk of radius 2
r-axis
(C)-
centered at the point
x = -2,
\y = 9 – V4- a², y = 9+ v4- x² )
I = 2
(a)
R =
(Ь)
Sketch of R
(c)
Sketch of S (a torus)
*[(19+ va= z²j² - [9 – va – 2² 1* ) dz
(d)
vol(S) =
IVA- z² dx = 72m².
= 367
(e)
vol(S) 710.61152.

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