In this lesson, you will learn to how to find the volume of a solid using the area of a cross-section.
Upon completion of the lesson 8.3, you will be able to use integration to calculate the volume of a solid given the areas of parallel cross sections.
View all of the following instructional videos. These will help you master the objectives for this module.
Volume calculations 1: Integration of Cross-sectional Area [University of Houston]
YouTube video: Volumes by Slicing
The following required readings cover the content for this module. As you go through each reading, pay close attention to the content that will help you learn the objectives for this module.
Make your way through each of the practice exercises. This is where you will take what you have learned from the lesson content and lesson readings and apply it by solving practice problems.
Volume by Parallel Cross Sections; Discs and Washers [University of Houston] (answers and solutions provided)
Note: Do problem #6 only.
Applications of the Definite Integral - Volume [Wake Forest University]
Note: Please read only section I - Volumes by Slicing. Then, go to page 10 where there is a Practice Sheet. Do problems #1 - 4. Answers and solutions are provided beginning on page 11.
More Volume Problems [Paul's Online Math Notes] (answers and solutions provided)
Below are additional resources that help reinforce the content for this module.
YouTube video: Volumes Using Cross Sectional Slices - Ex. 1
YouTube video: Volume of a Solid with Known Cross-Sections
Note: Read pp. 379-385 up to and including Practice 4. Do Practice 1 -4. The answers to the practice problems begin at the bottom of p. 392.