Determining the Surface Area of a Solid of Revolution - Page 6

Questions
  • What is the surface area of the solid created by revolving #f(x) = 2x^2-3x+22 , x in [2,3]# around the x axis?
  • What is the surface area of the solid created by revolving #f(x) = 1/(1-x), x in [2,5]# around the x axis?
  • What is the surface area of the solid created by revolving #f(x) = 3x, x in [2,5]# around the x axis?
  • How do you find the surface area of a solid of revolution?
  • What is the surface area produced by rotating #f(x)=cscxcotx, x in [pi/8,pi/4]# around the x-axis?
  • What is the surface area of the solid created by revolving #f(x) = e^(2x) , x in [2,7]# around the x axis?
  • How do you find the area of the surface generated by rotating the curve about the y-axis #y=1/3(x^2+2)^(3/2), 1<=x<=2#?
  • How do you find the area of the surface generated by rotating the curve about the x-axis #y=1/4x^4+1/8x^-2, 1<=x<=2#?
  • How do you find the surface area of the solid obtained by rotating about the #y#-axis the region bounded by #y=x^2# on the interval #1<=x<=2# ?
  • What is the surface area of the solid created by revolving #f(x)=xsqrt(x-1)# for #x in [2,3]# around the x-axis?
  • Optimization - Find the surface area of a domed cylinder?
  • Sketch the region enclosed by the curve and calculate it's area?
  • A poster whose area is #180# square inches, has #1# inch margin at bottom and on sides #2# inch margin at the top. What are its dimensions for which printed area is maximized?
  • Let R be the region bounded by y=4/(x^3), y=1/2 and x=1. What is R if it revolved around the line y = -2?
  • What are the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 484 meters?
  • Find the area of the largest rectangle having two vertices on the x axis and two more vertices above the x axis and on the parabola with equation y=9-x²?
  • Find a vector function, #r(t)#, that represents the curve of intersection of the two surfaces. The cylinder #x^2 + y^2 = 81# and the surface #z = xy#?
  • How do you find the area of the region bounded above by the parabola y=2-x^2, and below by the line y=-x' ?
  • The volume of a spherical ball increase at the rate of 4π cc/s . Then the rate of increase of the surface area when the volume is 288π cc ? a)4π/3 b)3π/2 c)6π d)6
  • The graph of the equation 2x=y^2 from A (0,0) to B (2,2) is revolved about the x-axis. The surface area of the resulting solid( in square units and to three decimal places) is ?