6.2 volumes part 2 washer method apr 5.notebook · 6.2 volumes part 2 washer method apr 5.notebook...
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6.2 Volumes Part 2 Washer Method Apr 5.notebook
1
April 05, 2017
6.2 Volumes Part 2: Washer Method
The disk method can be extended to cover solids of revolutions with holes by replacing the crosssection of a disk with crosssection of a washer via composite figures.
Consider: Determine the volume of the solid that is generated by revolving the region between and from to around the xaxis.
Disk Method "Composite Figures"
1 0 1 2 3 4
2
1
1
2
x
y
1 0 1 2 3 4
2
1
1
2
x
y
6.2 Volumes Part 2 Washer Method Apr 5.notebook
2
April 05, 2017
Washer Method
Case 1: Horizontal Axis of Revolution
Volumes Of Revolutions: Washer Method
Note: is the outer radius of the washer formed while is the inner radius.
Caution: [a,b] are horizontal endpoints. (xvalues)
6.2 Volumes Part 2 Washer Method Apr 5.notebook
3
April 05, 2017
Case 2: Horizontal Axis of Revolution
Note: is the outer radius of the washer formed while is the inner radius.
x
y
Caution: [c,d] are vertical endpoints. (yvalues)
Example 1: Find the volume of the solid formed by revolving the region bounded by the graphs of and .
1 0 1 2
2
1
1
2
x
y
Example 2: See Example 5 Text pg 423
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