Volume - with a representative washer. r w R Volume of...

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Volume: The Disc Volume: The Disc Method Method Section 7.2
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If a region in the plane is revolved about a line, the resulting solid is a solid of revolution , and the line is called the axis of revolution . The simplest such solid is a right circular cylinder or disc , which is formed by revolving a rectangle about an axis .
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R w Axis of Revolution w R
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The Disc Method The Disc Method Volume of disc = (area of disc)(width of disc) x r V = 2 π
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Horizontal Axis of Revolution Volume = V = Vertical Axis of Revolution Volume = V = [ ] dx x R b a 2 ) ( π [ ] dy y R d c 2 ) (
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The Washer Method The Washer Method The disc method can be extended to cover solids of revolution with holes by replacing the representative disc
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Unformatted text preview: with a representative washer. r w R Volume of washer = dx r R ) ( 2 2- [ ] [ ] ( 29 dx x r x R V b a -= 2 2 ) ( ) ( Volumes of Solids with Known Volumes of Solids with Known Cross Sections Cross Sections 1. For cross sections of area A(x) taken perpendicular to the x-axis, Volume = 2. For cross sections of area A(y) taken perpendicular to the y-axis, Volume = b a dx x A ) ( d c dy y A ) ( Joke Time Joke Time Why didnt the skeleton cross the road? He didnt have any guts! How do you make a tissue dance? Put some BOOGIE in it! Why do eskimos wash their clothes in Tide? Because it is too cold out tide....
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This note was uploaded on 12/01/2011 for the course MATH 112 taught by Professor Jarvis during the Fall '08 term at BYU.

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Volume - with a representative washer. r w R Volume of...

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