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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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 Fall '08
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 Math, Calculus, Euclidean geometry, wireless devices, Pappus Theorem, Form Pappus theorem

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