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 #39) 37. Consider the solid generegion in Exercise 1 about the line y = 2.(a) Make a conjecture as to which is larger: the volumeof this solid or the volume of the solid in Exercise 1,Explain the basis of your conjecture.(b) Check your conjecture by calculating this volumeand comparing it to the yolume obtained in Exer-cise 1.38. Consider the solid generated by revolving the shaded50. As shown in the accompanying figure, adesigned with three semicircular supporteach horizontal cross section is a regulthat the volume of the dome is r'V3.region in Exercise 4 about the line x= 2.5.(a) Make a conjecture as to which is larger: the volumeof this solid or the volume of the solid in Exercise 4.Explain the basis of your conjecture.(b) Check your conjecture by calculating this volumeand comparing it to the volume obtained in Exer-cise 4.Figure Ex-39. Find the volume of the solid that results when the regionenclosed by v = V, v = 0, and x = 9 is revolved aboutthe line x = 9.C 51-54 Use a CAS to estimate the volumsults when the region enclosed by the curthe stated axis.40. Find the volume of the solid that results when the region inExercise 39 is revolved about the line y = 3.41. Find the volume of the solid that results when the region51. y = sin° x, y = 2x/T, x = 0, x = T52. y = 7' sin x cos' x, y = 4x, x =53. y = e*, x = 1, y = 1; y-axis54. y = xVtan-x, y = x; x-axisenclosed by x = y? and x = y is revolved about the line55. The accompanying figure shows ap and heighth cut from a sphere ofvolume V of the spherical cap can(a) V = ah?(3r – h)y = -1.42. Find the volume of the solid that results when the region inExercise 41 is revolved about the line x = -1.(b)43. Find the volume of the solid that results when the regionenclosed by y = x' and y = x' is revolved about the linex= 1.44. Find the volume of the solid that results when the region inExercise 43 is revolved about the line y = -145. A nose cone for a space reentry vehičle is designed so thata cross section, taken x ft from the tip and perpendicular tothe axis of symmetry, is a circle of radius x ft. Find thevolume of the nose cone given that its length is 20 ft.Figure Ex-546. A certain solid is 1 ft high, and a horizontal cross sectiontaken x ft above the bottom of the solid is an annulus ofinner radius x² ft and outer radius Vx ft. Find the volume56. If fluid enters a hemispherical bea rate of ; ft'/min, how fast wthe depth is 5 ft? [Hìnt: See Ex57. The accompanying figure showlightbulb at 10 equally spaced(a) Use formulas from geomeof the volume enclosed by(b) Use the average of left antions to approximate theof the solid.47. Find the volume of the solid whose base is the regionbounded between the curves y = x and y = x', and whosecross sections perpendicular to the x-axis are squares.48. The base of a certain solid is the region enclosed by y =Vĩ, y = 0, and r = 4. Every cross section perpendicular tothe x-axis is a semicircle with its diameter across the base.Find the volume of the solid.49. In parts (a)-(c) find the volume of the solid whose base isenclosed by the circle x2 + y? = 1 and whose cross sec-tions taken perpendicular to the x-axis are(a) semicircles(c) equilateral triangles.2 N N N - -C-8-お_8_あ_あ_8.(b) squares5.5 cmA Figure Ex-57

Question

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 #39) 37. Consider the solid generegion in Exercise 1 about the line y = 2.(a) Make a conjecture as to which is larger: the volumeof this solid or the volume of the solid in Exercise 1,Explain the basis of your conjecture.(b) Check your conjecture by calculating this volumeand comparing it to the yolume obtained in Exer-cise 1.38. Consider the solid generated by revolving the shaded50. As shown in the accompanying figure, adesigned with three semicircular supporteach horizontal cross section is a regulthat the volume of the dome is r'V3.region in Exercise 4 about the line x= 2.5.(a) Make a conjecture as to which is larger: the volumeof this solid or the volume of the solid in Exercise 4.Explain the basis of your conjecture.(b) Check your conjecture by calculating this volumeand comparing it to the volume obtained in Exer-cise 4.Figure Ex-39. Find the volume of the solid that results when the regionenclosed by v = V, v = 0, and x = 9 is revolved aboutthe line x = 9.C 51-54 Use a CAS to estimate the volumsults when the region enclosed by the curthe stated axis.40. Find the volume of the solid that results when the region inExercise 39 is revolved about the line y = 3.41. Find the volume of the solid that results when the region51. y = sin° x, y = 2x/T, x = 0, x = T52. y = 7' sin x cos' x, y = 4x, x =53. y = e*, x = 1, y = 1; y-axis54. y = xVtan-x, y = x; x-axisenclosed by x = y? and x = y is revolved about the line55. The accompanying figure shows ap and heighth cut from a sphere ofvolume V of the spherical cap can(a) V = ah?(3r – h)y = -1.42. Find the volume of the solid that results when the region inExercise 41 is revolved about the line x = -1.(b)43. Find the volume of the solid that results when the regionenclosed by y = x' and y = x' is revolved about the linex= 1.44. Find the volume of the solid that results when the region inExercise 43 is revolved about the line y = -145. A nose cone for a space reentry vehičle is designed so thata cross section, taken x ft from the tip and perpendicular tothe axis of symmetry, is a circle of radius x ft. Find thevolume of the nose cone given that its length is 20 ft.Figure Ex-546. A certain solid is 1 ft high, and a horizontal cross sectiontaken x ft above the bottom of the solid is an annulus ofinner radius x² ft and outer radius Vx ft. Find the volume56. If fluid enters a hemispherical bea rate of ; ft'/min, how fast wthe depth is 5 ft? [Hìnt: See Ex57. The accompanying figure showlightbulb at 10 equally spaced(a) Use formulas from geomeof the volume enclosed by(b) Use the average of left antions to approximate theof the solid.47. Find the volume of the solid whose base is the regionbounded between the curves y = x and y = x', and whosecross sections perpendicular to the x-axis are squares.48. The base of a certain solid is the region enclosed by y =Vĩ, y = 0, and r = 4. Every cross section perpendicular tothe x-axis is a semicircle with its diameter across the base.Find the volume of the solid.49. In parts (a)-(c) find the volume of the solid whose base isenclosed by the circle x2 + y? = 1 and whose cross sec-tions taken perpendicular to the x-axis are(a) semicircles(c) equilateral triangles.2 N N N - -C-8-お_8_あ_あ_8.(b) squares5.5 cmA Figure Ex-57

Accepted Answer

Solution is here

D. 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. Find the yolume of the solid that results when the region in