Explanation Show the solid-shaded area is divided into four segments as in Figure 1. Show the shaded area for the 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 1.5 0.75 1.125 2 2 1

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Center of Gravity and Centroid

The term center of gravity indicates the position or location of a point about which the whole weight of a body or system is supposed to be concentrated, which means the whole weight of the body or system works through this point. It is closely related t…

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Chapter 9.3, Problem 13FP

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

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Chapter 9.2, Problem 89P

Chapter 9.3, Problem 14FP

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Chapter 9 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

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

Solution Summary: The author illustrates 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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