- A typical square cross section has side length and area .
- Possible numerical values of the -coordinates of points in the base range from a minimum value of up to a maximum of .
- To compute volume, integrate:

Exercises computing volume by cross-sectional area.

The base of a solid region is bounded by the curves , and . The cross sections
perpendicular to the -axis are squares. Compute the volume of the region.

A right circular cylinder of radius and height is twisted along its axis
so that the disk at height is centered on the axis , which corresponds to
one full twist along the axis. Compute the volume of this twisted cylinder.

A certain three-dimensional region has a base in the -plane which is bounded above
by the graph and below by . Slices perpendicular to the -axis are equilateral
triangles whose base lies in the -plane as well. Compute the volume of the region.

### Sample Exam Questions

(2018 Midterm 1) Compute the volume of the region in 3-dimensional space which
satisfies the inequalities

none of these