Problem 13 · 2022 Math Kangaroo
Hard
Geometry & Measurement
area
The diagram shows three big circles of equal size and four small circles. Each small circle touches two big circles and has radius 1. How big is the shaded area?
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Answer: B — \(2\pi\)
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Hint 1 of 2
The small circles have radius 1; relate the big-circle radius to the small ones.
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Hint 2 of 2
The shaded crescent-like pieces rearrange to a neat multiple of pi.
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Approach: express the shaded region using the small radius 1
- Each small circle has radius 1 and sits where two big circles meet.
- Adding and subtracting the overlapping circular regions, the shaded crescents combine to a clean area.
- The total shaded area equals 2*pi.
Mark:
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