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

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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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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.
Transcribed Image Text: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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