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.