1120_5 - Week 5 Outline More volumes by slicing Procedures...

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Week 5 Outline More volumes by slicing –Procedures of Calculating the volume of a Solid –Some examples that are not solids of revolution Compute the arc length of a curve –the definition of arc length –the formula of arc length Procedures of Calculating the Volume of a Solid (1) Sketch the solid and a typical cross-section. (2) Find a formula for A ( x ), the area of a typical cross-section. (3) Find the lower and upper limits of integration. (4) Integrate A ( x ). Cavalieri’s Principle Solids with equal altitudes and identical cross-sectional areas at each height have the same volume. Examples 1. A square of side length s lies in a plane perpendicular to a line L . One vertex of the square lies on L . As this square moves a distance h along L , the square turns one revolution about L to generate a corkscrew-like column with square cross-sections. (a) Find the volume of the column. (b) What will the volume be if the square turns twice instead of once?
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