Explanation Show the solid-shaded area is divided into four segments as in Figure 1. Show the shaded area for volume is divided into two segments as in Figure 2. Express the surface area of the entire body using the theorem of Pappus and Guldinus. A = θ × ∑ r ¯ L (I) Here, the surface area of revolution is A , the angle of revolution measured in radians is θ , the perpendicular distance from the axis of revolution to the centroid of the generating curve is r ¯ , and the length of the generating curve is L . Since the angle of revolution is measured in radians, θ = 2 π Substitute 2 π for θ in Equation (I). A = 2 π × ∑ r ¯ L (II) Express the volume of the entire body using the theorem of Pappus and Guldinus. V = θ × ∑ r ¯ A (III) Here, the generating area is A , the perpendicular distance from the axis of revolution to the centroid of the generating area is r ¯ , the volume of revolution is V , and the angle of revolution measured in radians is r . Since the angle of revolution is measured in radians, θ = 2 π Substitute 2 π for θ in Equation (III). V = 2 π × ∑ r ¯ A (IV) Conclusion: Refer to Figure 1 and use the spreadsheet to calculate the values of L , r ¯ , and r ¯ L for four segments as shown in Table 1. Segment L ( m ) r ¯ ( m ) r ¯ L ( m 2 ) 1 1.2 2 + 0.9 2 = 1.5 1.5 + ( 0.5 × 0.9 ) = 1.95 2.925 2 1.5 1.5 + 0.9 = 2.4 3

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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The surface area ( A ) and volume of the solid ( V ) .

Solution Summary: The author analyzes the surface area and volume of the solid using the theorem of Pappus and Guldinus.

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