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pinwheel

Above, we have a larger circle of $r=16$ with 8 equally spaced semicircles of radius=8. Each semicircle has one end on the larger circle's center and the other on the circumference of the larger circle. Find the perimeter of the shaded region.


The circumference of the larger circle is $32\pi$ and it's divided into 8 parts, which makes the part of the perimeter of the shaded region resting on the larger circle measure $4\pi$ units. Both semicircular arcs measure $\pi r_2$ units = $8\pi$ units. So we have a perimeter of $8\pi+8\pi+4\pi = 20\pi$.

I feel like I might be misinterpreting the question, though- can you think of any other ways to interpret the question?

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    $\begingroup$ I think you're right. $\endgroup$ – Myself Feb 2 '12 at 18:07

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