Solving a Trig Word Problem Involving Pipes

[Miike012]

Homework Statement

Six Identical pipes, each with radius of 1 foot are ties tightly together with a metal band... Find the length of the metal band...

I posted a picture...

My strategy is dividing the figure in half
Then finding the measure of the two arcs in red ( which should be equal)
Then finding the measure of the yellow line..
Once I find that... I can multiply it by three...
I am just not sure of how to do it...

 

[Char. Limit]

Well, it looks to me as if x=30 degrees, but that's just an educated guess. And I recommend dividing the yellow line into three parts, the part above the bottom left circle, the part above the middle left circle, and the part above the upper circle. The middle part has an easy to calculate length, and the two outer parts will require some knowledge of cosines and sines on a circle.

 

[osnarf]

This requires no trig. Just consider the outline. If you replace the straight segments with a single point, what are you left with?

So the length of the curved segments are taken care of. It's easy to see the straight lines are all the same length. So, just look at the bottom one. How does it compare to the radius of the pipes?