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41. Find the volume of the solid that results when the region enclosed by x= y and x = y is revolved about the line y = -1. 12. Find the volume of the solid that results when the region in

41. Find the volume of the solid that results when the region enclosed by x= y and x = y is revolved about the line y = -1. 12. Find the volume of the solid that results when the region in

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Determine  whether the statement is true or false. Assume that a solid S of  volume V is bounded by two parallel  planes  perpendicular to the x-axis at x=a and x=b and that for each x in [a,b], A(x) denotes the cross-sectional  area of S perpendicular to the x-axis. (Solve question #41)

38. Consider the solid generated by revolving the shaded 50. region in Exercise 4 about the line x = 2.5. (a) Make a conjecture as to which is larger: the volume of this solid or the volume of the solid in Exercise 4. Explain the basis of your conjecture. (b) Check your conjecture by calculating this volume and comparing it to the volume obtained in Exer- cise 4. C 5 39. Find the volume of the solid that results when the region enclosed by y = Vĩ, y = 0, and x = 9 is revolved about the line x =9. th %3D 40. Find the volume of the solid that results when the region in Exercise 39 is revolved about the line y = 3. 5 41. Find the volume of the solid that results when the region enclosed by x = y² and x = y is revolved about the line y= -1. 42. Find the volume of the solid that results when the region in Exercise 41 is revolved about the line x = -1. 43. Find the volume of the solid that results when the region enclosed by y = x² and y = x is revolved about the line x= 1. 44. Find the volume of the solid that results when the region in Exercise 43 is revolved about the line y = -1. 45. A nose cone for a space reentry vehicle is designed so that a cross section, taken x ft from the tip and perpendicular to the axis of symmetry, is a circle of radius x² ft. Find the volume of the nose cone given that its length is 20 ft. .2 46. A certain solid is 1 ft high, and a horizontal cross section taken x ft above the bottom of the solid is an annulus of inner radius x ft and outer radius Va ft. Find the volume 2 of the solid. 17. Find the volume of the solid whose base is the region bounded between the curves y = x and 2. = x´, and whose cross sections perpendicular to the x-axis are squares. 18. The base of a certain solid is the region enclosed by y =
Transcribed Image Text:38. Consider the solid generated by revolving the shaded 50. region in Exercise 4 about the line x = 2.5. (a) Make a conjecture as to which is larger: the volume of this solid or the volume of the solid in Exercise 4. Explain the basis of your conjecture. (b) Check your conjecture by calculating this volume and comparing it to the volume obtained in Exer- cise 4. C 5 39. Find the volume of the solid that results when the region enclosed by y = Vĩ, y = 0, and x = 9 is revolved about the line x =9. th %3D 40. Find the volume of the solid that results when the region in Exercise 39 is revolved about the line y = 3. 5 41. Find the volume of the solid that results when the region enclosed by x = y² and x = y is revolved about the line y= -1. 42. Find the volume of the solid that results when the region in Exercise 41 is revolved about the line x = -1. 43. Find the volume of the solid that results when the region enclosed by y = x² and y = x is revolved about the line x= 1. 44. Find the volume of the solid that results when the region in Exercise 43 is revolved about the line y = -1. 45. A nose cone for a space reentry vehicle is designed so that a cross section, taken x ft from the tip and perpendicular to the axis of symmetry, is a circle of radius x² ft. Find the volume of the nose cone given that its length is 20 ft. .2 46. A certain solid is 1 ft high, and a horizontal cross section taken x ft above the bottom of the solid is an annulus of inner radius x ft and outer radius Va ft. Find the volume 2 of the solid. 17. Find the volume of the solid whose base is the region bounded between the curves y = x and 2. = x´, and whose cross sections perpendicular to the x-axis are squares. 18. The base of a certain solid is the region enclosed by y =
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