1. 6.2 Solids of Revolution-Disk Method Warm Up
Find the Volume of the solid of revolution formed by rotating the enclosed region about the x-axis.
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2. 6.2 Solids of Revolution-Disk Method
Washer Method
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3. 6.2 Solids of Revolution-Disk Method
Find the Volume of the solid of revolution formed by rotating the enclosed region about the x-axis and the y-axis.
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4. 6.2 Solids of Revolution-Disk Method
Find the Volume of the solid of revolution formed by rotating the enclosed region about the x-axis and the y-axis.
(Work on next slide)
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6. 6.2 Solids of Revolution-Disk Method
Practice:
Pg #'s 7-10, 11b, 12a, odd
For #’s 23 and beyond, Show sketch of shaded region, setup, and solution for every problem.
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7. 6.2 Solids of Revolution-Disk Method
The region between the curve , and the
y-axis is revolved about the y-axis. Find the volume.
We use a horizontal disk.
The thickness is dy.
The radius is the x value of the function
volume of disk

8. and is revolved about the y-axis. Find the volume.
The region bounded by
and is revolved about the y-axis.
Find the volume.
If we use a horizontal slice:
The “disk” now has a hole in it, making it a “washer”.
The volume of the washer is:
outer
radius
inner
radius