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

INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)

14th Edition

ISBN: 9780133918922

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 9.3, Problem 14FP

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

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Chapter 9 Solutions

INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)

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

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