Volumes of solids of known cross-section

The  exercise appears under the Integral calculus Math Mission. This exercise finds the volume of solids by perpendicular cross sections.

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


 * 1) Find the volume of the solid: This problems asks for the volume of a general solid. The student is expected to find the answer and indicate it as prompted.Vosokcs2.png
 * 2) Find the right set up for the volume: This problem asks for the volume of a region of which cross sections are defined. The student is expected to select the correct set up for the volume of the solid.Vosokcs1.png

Strategies
Knowledge of volume method by cross sections and other properties of volume are encouraged to ensure success on this exercise.
 * 1) Some of the common cross sections that can occur are rectangles, triangles, and semi-circles.
 * 2) Drawing an arbitrary cross section can help to set up the initial integral.

Real-life Applications

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