Explanation Second theorem of Pappus states that "the volume of a solid of revolution generated by rotating a plane figure about an axis is equal to the product of the area of figure and the distance traveled by itscentroid about the given axis. Given: Vertices of the triangle which is to be rotated about y-axis are (1, 0), (3, 0), and (2, 2). Formula: Volume of solid of revolution = A*d Where A is area of the given figure and d is distance travelled by centroid of tringle in making a complete rotation about y axis. Calculation: T h e c e n t r o i d o f t h e t r i a n g l e = ( x 1 + x 2 + x 3 3 , y 1 + y 2 + y 3 3 ) = ( 1 + 3 + 2 3 , 0 + 0 + 2 3 ) = ( 2 , 2 3 ) Distance travelled by centroid in rotating about y axis, d

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 9, Problem 22CRE

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The formula for the volume of the solid of revolution obtained by rotating the triangle with vertices (1, 0), (3, 0), and (2, 2) about the y-axis using the Theorem of Pappus.

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Chapter 9, Problem 21CRE

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The formula for the volume of the solid of revolution obtained by rotating the triangle with vertices (1, 0), (3, 0), and (2, 2) about the y-axis using the Theorem of Pappus.

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The formula for the volume of the solid of revolution obtained by rotating the triangle with vertices (1, 0), (3, 0), and (2, 2) about the y-axis using the Theorem of Pappus.

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