# Determining the Volume of a Solid of Revolution - Page 5

Questions

- 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#; and #x = 4# rotated about #y=6#?
- What is the volume of the solid produced by revolving #f(x)=tanx, x in [0,pi/4] #around the x-axis?
- How do you find the volume bounded by #y=ln(x)# and the lines y=0, x=2 revolved about the y-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(16-x^2)# and the x axis 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 = 2 x^4#, y = 0, x = 1 revolved about the x=2?
- What is the difference between the shell method and disk method?
- How do you find the volume of the solid obtained by rotating the region bounded by the curves #y=2x^2+5#, and #y=x+3# and the y-axis, and #x=3# rotated around the x axis?
- How do you find the volume of a solid of revolution washer method?
- How do you find the volume of the solid generated by revolving the region bounded by the graphs #y=x^2, y=4x-x^2#, about the x-axis, the line y=3?
- What is the volume of the solid produced by revolving #f(x)=x^2-x+1, x in [1,3] #around #x=1#?
- What is the volume of the solid produced by revolving #f(x)=x^2+3x-sqrtx, x in [0,3] #around the x-axis?
- How do you know when to use the shell method or the disk method?
- Find the volume of the solid of revolution obtained by rotating the curve #x=3cos^3theta# , #y=3sin^3theta# about the #x# axis?
- What is the Volume of Revolution if the area bounded by the curve #y=x^2-4x# and the #x#-axis is is rotated 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 #x= y^2# #x= y+2# rotated about the y-axis?
- How do you find the volume of the solid generated by revolving the region bounded by the graphs #xy=6, y=2, y=6, x=6#, about the line x=6?
- Using disk or ring method, how do you find the volume of #y=x^(2)-x#, #y=3-x^(2)#, about #y=4#?
- How do you find the volume bounded by #y = 12 ln x#, the x-axis, the y-axis and the line y=12 ln14 revolved about the y-axis?
- What is the volume of the solid produced by revolving #f(x)=1/sqrt(1+x^2)# around the x-axis?
- What is the volume of the solid produced by revolving #f(x)=sqrt(81-x^2)# around the x-axis?