MATH 1501: WEEK 12

Topics for this week are:

• Computations of volumes, centroids and other geometric quantities

Text coverage:     Sections 6.4 - 6.6 of Salas, Hille, and Etgen

Online resources:

• Maple Worksheets
  • Rotations : When drawing a figure of revolution, there are several ideas that ar ise: What will the figure look like? What is the area of the resulting surface? What is the volume of the enclosed solid? All three questions are addressed in this worksheet.
  • The Theorem of Pappus : Suppose that the plane region R is revolved about the line L in the xy-plane. S uppose also that the line does not intersect the region. The volume of the solid generated is equal to the product of the area of R and the length of the circum ference of the circle traced by the centroid of R. This result of Pappus is illustrated in this worksheet.
• Animations
  • The student Robert Martoncik contributed an animation showing the Cylindrical shell method for finding the volume of revolution. This example requires an avi decoder; for example, Apple's QuickTime.

---

Last Modified: . School of Mathematics, Georgia Institute of Technology.