# Determining the Volume of a Solid of Revolution - Page 2

Questions

- How do you find the volume of the solid generated by revolving the region bounded by the graphs #y = 9 - x^2#, #y=0#, #x=2#, #x=3# about the y-axis?
- How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by #y=e^x#, x=0, and y=pi revolved about the x-axis?
- How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by #y = x^3#, y=0 , x=1 revolved about the y=1?
- How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by #x=4y^2#, y = 1, x = 0 revolved about the y-axis?
- How do you find the volume of the bounded region if #y = sinx#, #y = 0# from #x = pi/4#, #x = 3pi/4#, revolved around the y-axis?
- Let R be the region enclosed by f(x) = x^2 + 2 and g(x) = (x - 2)^2. What is the volume of the solid produced by revolving R around the x-axis and then the y-axis?
- What is the volume of the solid produced by revolving #f(x)=xe^x-(x/2)e^x, x in [2,7] #around the x-axis?
- How do I find the volume of the solid generated by revolving the region bounded by #y=e^x# and #y=4x+1# about the #x#-axis? The line #y=12#?
- How do you find the volume of the solid generated by revolving the region bounded by the curves y = x^(1/2), y = 2, and x = 0 rotated about the x=-1?
- How do you find the volume of the solid generated by revolving the region bounded by the graphs #y=e^-x, y=0, x=0, x=1#, about the x axis?
- How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region #y = sqrt(x#), #y = 0#, #y = 12 - x# rotated about the x axis?
- How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by #y=8 sqrt x#, y=0, x=1 revolved about the x=-4?
- How do you find the volume bounded by #f(x) = x^2 + 1# and #g(x) = x + 3# revolved about the x-axis?
- How do you find the volume of the solid obtained by rotating the region bounded by the curves #1/(1+x^2)#, #y=0#, #x=0#, and #x=2# rotated around the #x=2#?
- Let R be the region enclosed by #y= e^(2x), y=0, and y=2#. What is the volume of the solid produced by revolving R around the x-axis?
- How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region # y = x^3#, #y = 0#, #x = 2# rotated about the y axis?
- Find the volume using cylindrical shells? (Enclosed by x-axis and parabola #y=3x-x^2#, revolved about #x=-1#)
- Find the volume of the region bounded by y=sqrt(z-x^2) and x^2+y^2+2z=12?
- How do you find the volume of the region bounded #y = x²# and #y =1# is revolved about the line# y = -2#?
- How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region #y=2-x#, #2<=x<=4# rotated about the x-axis?