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The figure at the right shows three circular pipes all with 12inch diameters the have been strapped together by a metal band.What is the lenght of the band?

The figure at the right shows three circular pipes all with 12inch diameters the have been strapped together by a metal band.What is the lenght of the band?

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Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
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The band consists of three congruent segments with 2r each, and three congruent arcs with 120o each. So, the length of the band is

3[2r + (1/3)2pi r]

= 6r + 2pi*r

= 36 + 12pi inches, since r = 6 inches