5.2-5.3 Volumes

5.2-5.3 Volumes - Volumes Cross Sections Disk Method Shell...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Volumes Cross Sections, Disk Method, Shell Method Section 5.2 – 5.3 Volumes of Solids with Known 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 ) ( 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 disk , which is formed by revolving a rectangle about an axis . R w Axis of Revolution w R 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 = The representative rectangle is always perpendicular to the axis of revolution. [ ] dx x R b a 2 ) ( ∫ π [ ] dy y R d c 2 ) ( ∫ π The Washer Method The disc method can be extended to cover solids of revolution with holes by replacing the representative disc with a representative washer....
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 / 14

5.2-5.3 Volumes - Volumes Cross Sections Disk Method Shell...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online