# Calculating Volume using Integrals - Page 4

Questions

- How do you find the volume of the solid bounded by the coordinate planes and the plane #8x + 6y + z = 6#?
- The base of a certain solid is the triangle with vertices at (-8,4), (4,4), and the origin. Cross-sections perpendicular to the y-axis are squares. How do you find the volume of the solid?
- How would you find the volume bounded by the coordinate planes and by the plane 3x + 2y + 2z = 6?
- How do you find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes, and one vertex in the plane x+7y+11z=77?
- How do you find the volume of the solid bounded by the coordinate planes and the plane 3x + 2y + z = 6?
- The region is bounded by the given curves #y=0, y=sqrt(4-x^2), 0<=x<=1# is roated about the x-axis, how do you find the volume of the two solids of revolution?
- Calculate the volume of a solid whose base is the ellipse # 4x^2 + y^2 = 4 # and has vertical cross sections that are square?
- How do you find the volume of a solid that is enclosed by #y=2x+2# and #y=x^2+2# revolved about the x-axis?
- How do you use the Disk method to set up the integral to find the volume of the solid generated by revolving about the y-axis the region bounded by the graphs of and the line #y = x#, and #y = x^3# between x = 0 and x = 1?
- The base of a solid is the region in the first quadrant bounded by the line x+2y=4 and the coordinate axes, what is the volume of the solid if every cross section perpendicular to the x-axis is a semicircle?
- How would you find the volume of the tetrahedron T bounded by the coordinate planes and the plane 3x+4y+z=10?
- How do you find the volume of the solid bounded by Z = 1 – y^2, x + y = 1, and the three coordinate plane?
- The region under the curves #y=3/4x, y=1-x, y=x-1/x# is rotated about a) the x axis and b) the y axis. How do you sketch the region and find the volumes of the two solids of revolution?
- How do you use the triple integral to find the volume of the solid in the first octant bounded by the coordinate planes and the plane 3x+6y+4z=12?
- How do you find the volume of the solid bounded by the coordinate planes and the plane #2x+y+z=3#?
- The region under the curves #1/(x^2+1)=y, 0<=x<=2# is rotated about the x axis. How do you find the volumes of the two solids of revolution?
- How do you find the volume of the solid with base region bounded by the curve #y=1-x^2# and the #x#-axis if cross sections perpendicular to the #x#-axis are isosceles triangles with height equal base?
- Let R be the region in the first quadrant enclosed by the graph of #y=2cosx#, the x-axis, and the y-axis, how do you find the volume of the solid obtained by revolving region R about the x-axis?
- How do you find the volume of the solid bounded by the coordinate planes and the plane #7x+y+z=4#?
- How do you find the volume of the solid tetrahedron bounded by the coordinate planes and the plane x + 3y + z = 6?