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

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Chapter 9, Problem 28CRE

To determine

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 27CRE

Chapter 10.1, Problem 1PQ

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Ch. 9.1 - Prob. 1PQ Ch. 9.1 - Prob. 2PQ Ch. 9.1 - Prob. 3PQ Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E

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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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