Explanation Given: The outer surface of the ring ( b ) is 8 in. The inner surface of the ring ( a ) is 4 in. Explanation: Draw the free body diagram of the ring as in Figure 1. Calculate the radius of the pipe by considering the cross section of the pipe. r p i p e = b − a a (I) Calculate the perimeter of the cross section of the pipe. P p i p e = 2 π r p i p e (II) Calculate the radius of the ring by considering the cross section. r r i n g = a 2 + b − a a (III) Calculate the perimeter of the cross section of the ring. P r i n g = 2 π r r i n g (IV) Express the surface area of the ring. A = P p i p e × P r i n g (V) Conclusion: Substitute 8 in. for b and 4 in. for a in Equation (I). r p i p e = 8 in . − 4 in . 4 in . = 1 in . Substitute 1 in. for r p i p e in Equation (II). P p i p e = 2 π ( 1 in . ) = 2 π in

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 9.3, Problem 102P

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The surface area of the ring ( A ) .

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