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Unformatted text preview: 1 ! = 1 3 . Observe that A is symmetric with respect to the x axis and the vertical line x = 1 / 2 so that the centroid of A is ¯ x1 / 2 and ¯ y = 0. Form Pappus theorem it follows that Vol( S ) = 2 π ¯ x Area( A ) = π 3 . Without using Pappus Theorem, the volume can be computed with the shells method and is given by Vol( S ) = 4 π Z 1 x 2 (1x ) dx = 4 π ˆ x 3 3 ﬂ ﬂ ﬂ ﬂ 1x 4 4 ﬂ ﬂ ﬂ ﬂ 1 ! = π 3 . Page 1 of 1...
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This note was uploaded on 05/23/2010 for the course MATH 1501 taught by Professor N/a during the Fall '08 term at Georgia Tech.
 Fall '08
 N/A
 Math, Calculus

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