# Determining the Volume of a Solid of Revolution - Page 4

Questions

- What is the volume of the solid produced by revolving #f(x)=sinx, x in [0,pi] #around the x-axis?
- How do you find the volume bounded by #x^2=4y# and the line x=2y revolved about the x-axis?
- Equilateral hexagon is revolving around one of its edges. Find the volume of the solid of revolution?
- How do you find the volume of the solid obtained by rotating the region bounded by the curves #y=4x-x^2# and #y=2-x# about the x axis?
- If #f (x)= x^2+ 1# , how do you find the volume of the solid generated by revolving the region under graph of f from x=-1 to x=1 about the x- axis?
- How to find the volume of the solid obtained by rotating the region bounded by the given curves about the line x=6. x=y^4 , x=1 ?
- How do you find the volume of the torus formed by revolving #(x-2)^2 +y^2=1# 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=x^6# and #y=sin((pix)/2)# is rotated about the line x=-4?
- What is the volume of the solid produced by revolving #f(x)=x^3, x in [0,3] #around #y=-1#?
- How do you find the volume of the region enclosed by the curves #y=x#, #y=-x#, and #x=1# rotated about the y axis?
- How do you find the volume of the solid generated by revolving the region bounded by the graphs #y=2x^2, y=0, x=2#, about the x-axis, y-axis, the line y=8, the line x=2?
- How do you find the volume of the solid obtained by rotating the region bounded by: #y=sqrt(x-1)#, y=0, x=5 rotated about y=7?
- 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=6# and #x=7-(y-1)^2# 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#, #y=0#, and #y=sqr2# rotated about the x axis?
- What is the volume of the solid produced by revolving #f(x)=x^3-2x+3, x in [0,1] #around the x-axis?
- From a unit sphere, the part between two parallel planes equidistant from the center, and with spacing 1 unit in-between, is removed. The remaining parts are joined together face-to-face, precisely. How do you find the volume of this new solid?
- What is the volume of the solid produced by revolving #f(x)=sqrt(1-x), x in [0,1] #around the x-axis?
- How do you use cylindrical shells to find the volume of a solid of revolution?
- How do you find the volume of the solid generated by revolving the region bounded by the curves y = 10 / x², y = 0, x = 1, x = 5 rotated about the x-axis?
- How do you find the volume of the region below #y= -3x+6# and enclosed by the y-axis from 0 to 2, rotated about the x-axis?