Page 89 - Calc for the Clueless

Following the section on volumes of rotations, some of the students wondered if you always have a π when you
do volumes by sections. These two additional examples deal with that question.

Example 15—

Base x + y = 9. Sections perpendicular to the x axis are equilateral triangles. Find the volume.
2
2

Even though the base is a circle, we are adding triangular slices. Since the area of a triangle does not involve π,
neither does our volume.

Example 16—

½
Base bounded by y - x , x = 9, x axis. Sections perpendicular to the x axis are semicircles. Find the volume.