Mr Hickman's Class 2022-2023
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Volume Through Integration


Volume Through Revolution of a Solid
Washer and Disk Method


Types of Problems:

Using Integration to determine the volumes of solids that are created through revolution about the x axis
Using Integration to determine the volumes of solids that are created through revolution about a horizontal line
Using Integration to determine the volumes of solids that are created through revolution about the y axis
Using Integration to determine the volumes of solids that are created through revolution about a vertical line

Homework & Practice

5-1-19 Volume by disk and washer about x and y axis
BLANK COPY
5-1-19 Volume by disk and washer about x and y axis
WORKED OUT SOLUTIONS

GEOGEBRA Link to #1
PROBLEM 1 LINK
GEOGEBRA Link to #3
​PROBLEM #3 Link
GEOGEBRA Link to #5
PROBLEM 5 Link 
GEOGEBRA Link to #6
PROBLEM #6 Link
5-3-19 Volume by disk and washer about NOT x and y axis
BLANK COPY

Video and other resources​

Animation of Volume by Revolution about x axis
YOU TUBE Video 1
Professor Dave Explains 
This video does an excellent job introducing the topic of volume by solids of revolution (in about 12 minutes)
YOU TUBE Video 2
Disk & Washer Method
LONG Video good worked out examples
​(almost 2 hours long )
YOU TUBE Video 3
Professor Leonard Explains 
Another good video that has worked out examples
LONG LONG VIDEO (almost 3 hours)
YOU TUBE Video 4
Other Resources
Rotating region about a line that is NOT an axes (washer method)
YOU TUBE Video 5

Desmos Files

​THIS REVOLVES ABOUT X AXIS
DESMOS LINK
Mr. Hickman Explains HOW
I made a video to show you how to use the DESMOS File above
(11 minutes)
MR H VIDEO 1
THIS REVOLVES ABOUT Y AXIS
DESMOS LINK 

Geogebra Files


Volume by Cross Sections

Types of Problems

Determine the volume associated with types of shapes created by a shaded region and semicircles, squares, isosceles right triangles, rectangles, and equilateral triangles

Homework & Practice

5-6-19 Volume by Cross Sections
BLANK COPY

Video and other resources

This is the source of the 5-6-19 problems 
YOU TUBE Video #1
GEOGEBRA Link 
This shows one example (squares) of a fixed cross section
GEOGEBRA Link #1 

Volume through Cylinders
Shell Method

​Types of Problems:

Homework & Practice

Video and other resources

Professor Dave Explains
(8 minutes)
YOU TUBE Video 1
Shell Method
LONG Video good worked out examples
(55 minutes)
YOU TUBE Video 2
Volumes by Shells
(12 minutes)
YOU TUBE Video 3
Professor Leonard Explains
​(55 minutes)
YOU TUBE Video 4


Additional Resources


Mr Hickman is available for assistance after school practically anytime.  Talk to me to be certain that I am aware you are coming and 99% of the time I will be able to help you