6 2 volumes l.jpg
This presentation is the property of its rightful owner.
Sponsored Links
1 / 6

6.2 Volumes PowerPoint PPT Presentation


  • 109 Views
  • Uploaded on
  • Presentation posted in: General

6.2 Volumes. If a region in the plane is revolved about a line, the resulting solid is called a solid of revolution , the line is called the axis of revolution . The Disc Method The Washer Method. the strip is perpendicular to the axis of revolution. A. Volume: The Disc Method.

Download Presentation

6.2 Volumes

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


6 2 volumes l.jpg

6.2 Volumes

If a region in the plane is revolved about a line, the resulting solid is called a solid of revolution, the line is called the axis of revolution.

  • The Disc Method

  • The Washer Method

the strip is perpendicular to the axis of revolution


A volume the disc method l.jpg

A. Volume: The Disc Method

Vertical Strip

Typical disc

Plane Region

r

Axis of Revolution

x=a

x= b

Volume of Typical Disc

Solid of Revolution

where r = radius

Volume of Solid


B volume the washer method l.jpg

B. Volume: The Washer Method

Typical Washer

Vertical Strip

Plane Region

Solid of Revolution

Axis of Revolution

a

b

Volume of Typical Washer

where

= outer radius

= inner radius

Volume of Solid


Examples l.jpg

Examples

Find the exact volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disc or washer.

Example One:

about the y-axis

Example Two:

about


Slide5 l.jpg

Solutions: Example One

Graph is a parabola with vertex of (1/4,1/2)

y

y

By disc method

1

(1/4,1/2)

r

x

x

0


Slide6 l.jpg

Solutions: Example Two

y

y

x

x

1

3

By washer method


  • Login