Problem 18 · 2010 Math Kangaroo
Medium
Geometry & Measurement
perimeterarea-decomposition
A circle of radius 4 cm is divided, as shown, by four semicircles of radius 2 cm into four congruent parts. What is the perimeter of one of these parts?
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Answer: C — \(6\pi\)
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Hint 1 of 2
The boundary of one piece is made of arcs - part of the big circle plus the small semicircle arcs.
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Hint 2 of 2
Add up the arc lengths; the arc of a half-circle of radius 2 has length pi times 2.
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Approach: add the arc lengths of one piece
- The outer edge of one piece is a quarter of the big circle: (1/4) x 2pi x 4 = 2pi.
- Its inner edge is two semicircle arcs of radius 2, each pi x 2 = 2pi.
- Total perimeter = 2pi + 2pi + 2pi = 6pi.
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