COSMOS Chapter 9 Solution 29 - Edubirdie

University:
Michigan State University
Course:
ERG 160 | Success in Science, Technology, Engineering, and Mathematics
Academic year:

2023
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83

Pages:

1
Author:

Kundulu8mbj

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 29. First the circular area is divided into an increasing number of identical circular sectors. The sectors can be approximated by isosceles triangles. For a large number of sectors the approximate dimensions of one of the isosceles triangles are as shown. For an isosceles triangle (see Problem 9.28) JO = b = r ∆θ Then with = dJ O sector dθ ) h=r and 1 4  r ∆θ 12 + ∆θ 2    48 ( )  ∆ J O sector  2  1 4 = lim   = lim  r 12 + ( ∆θ )   ∆θ → 0   ∆θ  ∆θ → 0  48 = Then ( 1 ( r ∆θ )( r ) 12r 2 + ( r ∆θ )2  48 ( ∆ J O )sector Now bh 12h 2 + b 2 48 1 4 r 4 ( J O )circle 2π = ∫ dJ O sector = ∫ 0 1 4 1 2π r dθ = r 4 [θ ]0 4 4 or ( J O )circle = π 2 r4

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