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Unformatted text preview: ways, but the simplest cross section is a rectangle. If we let h equal the height of the slice then the volume of the slice is: ( 29 2 V x y h dx = Since the wedge is cut at a 45 o angle: x h 45 o h x = Since 2 2 9 x y + = 2 9 y x = x y ( 29 2 V x y h dx = h x = 2 9 y x =( 29 2 2 9 V x x x dx = 3 2 2 9 V x x dx = 2 9 u x = 2 du x dx = ( 29 9 u = ( 29 3 u = 1 2 9 V u du =  9 3 2 2 3 u = 2 27 3 = 18 = Even though we started with a cylinder, does not enter the calculation! Cavalieris Theorem: Two solids with equal altitudes and identical parallel cross sections have the same volume. Identical Cross Sections...
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This note was uploaded on 03/10/2008 for the course MATH 214 taught by Professor Riggs during the Fall '05 term at Cal Poly Pomona.
 Fall '05
 Riggs
 Differential Calculus

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