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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 xaxis, Volume = 2. For cross sections of area A(y) taken perpendicular to the yaxis, 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....
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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.
 Fall '08
 JARVIS
 Calculus, Disk Method, Shell Method

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