# Determining the Volume of a Solid of Revolution - Page 6

Questions

- How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by #y = 32 - x^2# and #y= x^2# revolved about the x=4?
- What is the volume of the solid produced by revolving #f(x)=cscx-cotx, x in [pi/8,pi/3] #around the x-axis?
- What is the volume obtained by rotating the region enclosed by #y=11-x#, #y=3x+7#, and #x=0# 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=4x-x^2#, y=3 revolved about the x=1?
- How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by #y=3x^4#, y=0, x=2 revolved about the x=4?
- If R is the area enclosed by f(x) and g(x), is the volume of the solid generated by revolving R around the x-axis then revolving that solid around the y-axis equal to the volume of the solid generated if the order of the revolutions was switched?
- How do you find the volume of the solid obtained by rotating the region bounded by the curves #x=y# and #y=sqrtx # about the line #x=2#?
- How do you find the volume of #y=3/(x+1)#, #y=0#; #x=0#; #x= 8# rotated around the x-axis?
- How do you find the volume of the solid generated by revolving the region bounded by #y=2x^2#, #y=0#, #x=2#, revolving on #y=8#?
- How do you find the volume of the region enclosed by the curves #y=2x#, #y=x#, and #y=4# is revolved about the y-axis?
- How do you find the volume of the solid generated by revolving the region bounded by the curves #y=x^(2)-x#, #y=3-x^(2)# rotated about the #y=4#?
- Y=sqrt(x), y=0, x=0,and x=2 a. Find the area of the region b. find the volume of the solid formed by rotating the region about the x-axis c. find the volume of the solid?
- How do you find the volume of the solid generated by revolving the region bounded by the curves y = x² and y =1 rotated about the y=-2?
- How do you find the volume bounded by #y^2=x^3-3x^2+4# & the lines x=0, y=0 revolved about the x-axis?
- How do you use the disk or shell method to find the volume of the solid generated by revolving the regions bounded by the graphs of #y = x^(1/2)#, #y = 2#, and #x = 0# about the line #x = -1#?
- How do you find the volume bounded by #y^2=x^3# and #y=x^2# revolved about the y-axis?
- What is the volume of the solid produced by revolving #f(x)=5x, x in [0,7] #around the x-axis?
- What is the volume of the solid produced by revolving #f(x)=sqrt(1+x^2)# around the x-axis?
- How do you find the volume of the solid generated by revolving the region bounded by the graphs #x=y^2, x=4#, about the line x=6?
- How do you find the volume of the region enclosed by the curves #y = x^2 - 1# and #y =0# rotated around the line #x = 5#?