6.2 Solids of Revolution-Disk Method Warm Up

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Presentation transcript:

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. 4/28/2019

6.2 Solids of Revolution-Disk Method Washer Method 4/28/2019

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. 4/28/2019

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) 4/28/2019

6.2 Solids of Revolution-Disk Method Practice: Pg. 428 #'s 7-10, 11b, 12a, 31-35 odd For #’s 23 and beyond, Show sketch of shaded region, setup, and solution for every problem. 4/28/2019

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

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