Volume

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

This preview shows pages 1–11. Sign up to view the full content.

Volume: The Disc Volume: The Disc Method Method Section 7.2

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 .
R w Axis of Revolution w R

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The Disc Method The Disc Method Volume of disc = (area of disc)(width of disc) x r V = 2 π
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 ) (

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The Washer Method The Washer Method The disc method can be extended to cover solids of revolution with holes by replacing the representative disc

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

## This note was uploaded on 12/01/2011 for the course MATH 112 taught by Professor Jarvis during the Fall '08 term at BYU.

### Page1 / 11

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

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online