# Calculating Volume using Integrals - Page 2

Questions

- How do you find the volume of a solid that is enclosed by #y=1/x#, x=1, x=3, y=0 revolved about the y axis?
- How do you find the volume of the solid bounded by the coordinate planes and the plane #5x + 5y + z = 6#?
- Let R be the region enclosed by the graphs of #y=(64x)^(1/4)# and #y=x#. How do you find the volume of the solid generated when region R is revolved about the x-axis?
- The tetrahedron enclosed by the coordinates planes and the plane 2x+y+z=4, how do you find the volume?
- How do you find the volume of the solid bounded by the coordinate planes and the plane #3x+2y+z=1#?
- The region under the curves #y=1/sqrtx, 1<=x<=2# is rotated about the x axis. How do you sketch the region and find the volumes of the two solids of revolution?
- How do you find the volume of a solid that is enclosed by #y=x^2-2#, #y=-2#, and #x=2# revolved about y=-2?
- How do you find the volume of the resulting solid by any method of #x^2+(y-1)^2=1 # about the x-axis?
- How do you use the triple integral to find the volume of the solid bounded by the surface #z=sqrt y# and the planes x+y=1, x=0, z=0?
- The base of a solid is a region in the first quadrant bounded by the x-axis, the y-axis, and he line x+2y=8. If the cross sections of the solid perpendicular to the x-axis are semicircles, what is the volume of the solid?
- How do you find the volume of the solid enclosed by the surface z=xsec^2(y) and the planes z=0, x=0,x=2,y=0, and y=π/4?
- The region under the curves #y=sqrt((2x)/(x+1)), 0<=x<=1# is rotated about the x axis. How do you sketch the region and find the volumes of the two solids of revolution?
- How do you use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the given plane #x + 8y + 7z = 24#?
- How do you find the volume of the solid generated when the regions bounded by the graphs of the given equations #y = root3x#, x = 0, x = 8 and the x-axis are rotated about the x-axis?
- Let R be the region between the graphs of #y=1# and #y=sinx# from x=0 to x=pi/2, how do you find the volume of region R revolved about the x-axis?
- The region is bounded by the given curves #y=x, y=4-x, 0<=x<=2# is rotated about the x-axis, how do you find the volume of the two solids of revolution?
- How do you compute the volume of the solid formed by revolving the given the region bounded by #y=sqrtx, y=2, x=0# revolved about (a) the y-axis; (b) x=4?
- How do you find the volume of the parallelepiped with adjacent edges pq, pr, and ps where p(3,0,1), q(-1,2,5), r(5,1,-1) and s(0,4,2)?
- How do you find the volume of the solid generated by revolving the region bounded by the graphs of the equations #y=sqrtx#, y=0, and x=4 about the y-axis?
- The region under the curve #y=lnx/x^2, 1<=x<=2# is rotated about the x axis. How do you find the volume of the solid of revolution?