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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, π does not enter the calculation! → Cavalieri’s Theorem: Two solids with equal altitudes and identical parallel cross sections have the same volume. Identical Cross Sections π...
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 Fall '05
 Riggs
 Differential Calculus, Little Rock, Little Rock Central High School, Hanford High School, Vickie Kelly

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