Explanation Show the quarter circular area is divided into three segments as in Figure 1. Express the surface area of the ring 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 rad Substitute 2 π rad for θ in Equation (I). A = 2 π × ∑ r ¯ L (II) Conclusion: Refer to Figure 1 and use spreadsheet to calculate the values of L , r ¯ , and r ¯ L for three segments as shown in Table 1. Segment L ( ft ) r ¯ ( ft ) r ¯ L ( ft 2 ) 1 a 2 a 2 a 2 2 π a

Engineering Mechanics: Statics and Modified Mastering Engineering with eText and Access Card (14th Edition)

14th Edition

ISBN: 9780134229287

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 9.3, Problem 96P

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The surface area of the ring (A) .

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Chapter 9 Solutions

Engineering Mechanics: Statics and Modified Mastering Engineering with eText and Access Card (14th Edition)

Ch. 9.1 - In each case, use the element shown and specify...Ch. 9.1 - Determine the centroid (x,y) of the shaded area....Ch. 9.1 - Determine the centroid (x,y) of the shaded area....Ch. 9.1 - Determine the centroid of the shaded area. Prob....Ch. 9.1 - Locate the center of mass x of the straight rod if...Ch. 9.1 - Locate the centroid of the homogeneous solid...Ch. 9.1 - Locate the centroid z of the homogeneous solid...Ch. 9.1 - Locate the center of mass of the homogeneous rod...Ch. 9.1 - Determine the location (x,y) of the centroid of...Ch. 9.1 - If the rod has a weight per unit length of 100...

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The surface area of the ring ( A ) .

Solution Summary: The author explains the surface area of the ring using the theorem of Pappus and Guldinus.

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