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# 6.2 Volumes - PowerPoint PPT Presentation

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.

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## PowerPoint Slideshow about '6.2 Volumes' - viho

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Presentation Transcript

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

Vertical Strip

Typical disc

Plane Region

r

Axis of Revolution

x=a

x= b

Volume of Typical Disc

Solid of Revolution

Volume of Solid

Typical Washer

Vertical Strip

Plane Region

Solid of Revolution

Axis of Revolution

a

b

Volume of Typical Washer

where

Volume of Solid

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:

Example Two:

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

y

y

x

x

1

3

By washer method