Volumes-by-Cross-Sections
Review
The
following questions refer to the first-quadrant region bounded by and .
Set-up but do not evaluate the integrals.
1. Find the volume of the region generated when rotated about the x-axis.
2. Find the volume of the region generated when rotated about the y-axis.
3. Find the volume of the region generated when rotated about y = -2.
4. Find the volume when cross-sections perpendicular to the x-axis are sides of squares.
5. Find the volume of the region generated when rotated about x = 2.
6. Find the volume when cross-sections perpendicular to the y-axis are legs of isosceles right triangles.
7. Find the volume of the region generated when rotated about y = 5.
8. Find the volume when cross-sections perpendicular to the x-axis are diameters of circles.
9. Find the volume of the region generated when rotated about x = -3.
10. Find the volume when cross-sections perpendicular to the y-axis are sides of squares.