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34. When the ellipse consisting of all points (x, y) with x/a* + y*/6* = 1 is rotated around the horizontal axis we obtain an "ellipsoid of revolu- tion" (Figure 2). Find the volume of the enclosed solid.

34. When the ellipse consisting of all points (x, y) with x/a* + y*/6* = 1 is rotated around the horizontal axis we obtain an "ellipsoid of revolu- tion" (Figure 2). Find the volume of the enclosed solid.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Please solve 34 only

31. In the Appendix to Chapter 12 we described the cycloid, which has the parametric representation * = u(t) = a(t – sin t), y = v(t) = a(1 – cos t). (a) Find the length of one arch of the cycloid. [Answer: 8a). (b) Recall that the cycloid is the graph of v o u. Find the area under one arch of the cycloid by using the appropriate substitution in f and evaluating the resultant integral. (Answer: 3ma| Problems 32 through 44 use the material from Appendix 2 to Chapter 13. 32. (a) Find the volume of the solid obtained by revolving the region bounded by the graphs of f(x) = x and f(x) = x' around the hori- zontal axis. (b) Find the volume of the solid obtained by revolving this same region around the vertical axis. 33. Find the volume of a sphere of radius r. 34. When the ellipse consisting of all points (x, y) with x/a + y*/6? = 1 is rotated around the horizontal axis we obtain an "ellipsoid of revolu- tion" (Figure 2). Find the volume of the enclosed solid. FIGURE 2
Transcribed Image Text:31. In the Appendix to Chapter 12 we described the cycloid, which has the parametric representation * = u(t) = a(t – sin t), y = v(t) = a(1 – cos t). (a) Find the length of one arch of the cycloid. [Answer: 8a). (b) Recall that the cycloid is the graph of v o u. Find the area under one arch of the cycloid by using the appropriate substitution in f and evaluating the resultant integral. (Answer: 3ma| Problems 32 through 44 use the material from Appendix 2 to Chapter 13. 32. (a) Find the volume of the solid obtained by revolving the region bounded by the graphs of f(x) = x and f(x) = x' around the hori- zontal axis. (b) Find the volume of the solid obtained by revolving this same region around the vertical axis. 33. Find the volume of a sphere of radius r. 34. When the ellipse consisting of all points (x, y) with x/a + y*/6? = 1 is rotated around the horizontal axis we obtain an "ellipsoid of revolu- tion" (Figure 2). Find the volume of the enclosed solid. FIGURE 2
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