AP Calculus AB and BC glossary
Volume by cross sections
Volume by cross sections integrates the area of each slice along an axis. The slices are a stated shape such as a square, a semicircle, or an equilateral triangle built on a base region, and no rotation is involved at all.
The whole task is writing the side length in terms of x, usually as the distance between two curves, then putting it into the area formula for the named shape before integrating.
The mistake
Using the radius where the diameter belongs. For a semicircular cross section on a base, the distance between the curves is usually the diameter, so the radius is half of it.
Appears in: Unit 8: Applications of Integration