Volumes of solids of revolution by shells

The  exercise appears under the Integral calculus Math Mission. This exercise finds the volume of a solid of revolution.

Types of Problems
There are three types of problems in this exercise:


 * 1) Match the formula with the region: This problem has a diagram and various integrals that represent volumes of different solids. The student is expected to match the appropriate integral with each labeled region.Vosorbs1.png
 * 2) Find the volume of the solid: This problems asks for the volume of a rotation. The student is expected to find the answer and indicate it as prompted.Vosorbs3.png
 * 3) Find the right set up for the volume: This problem asks for the volume of a region rotated about an axis. The student is expected to select the correct set up for the given solid.Vosorbs2.png

Strategies
Knowledge of volume method of cylindrical shells and other properties of volume are encouraged to ensure success on this exercise.
 * 1) The cylindrical shell method uses the lateral area of a cylinder, given by 2\pi*r*h.
 * 2) The formulaic shell method is integral from a to b of 2\pih(x)(x-c).
 * 3) Some regions can be changed from shell methods into disk methods and vice versa.

Real-life Applications

 * 1) Volume formulas for various 3D shapes can be developed by the methods done in this exercise.