Unformatted text preview: 9.9 . 20 ............................................................................................................... Figure 9.9 A region that generates a cone; approximating the volume by circular disks. ( JA ) At a particular point on the xaxis, say x i , the radius of the resulting cone is the ycoordinate of the corresponding point on the line, namely y i = x i / 2. Thus the total volume is approximately n1 X i =0 π ( x i / 2) 2 dx and the exact volume is Z 20 π x 2 4 dx = π 4 20 3 3 = 2000 π 3 . Note that we can instead do the calculation with a generic height and radius: Z h π r 2 h 2 x 2 dx = πr 2 h 2 h 3 3 = πr 2 h 3 ,...
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 Spring '07
 JonathanRogawski
 Math, Calculus, ........, π

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