Problem 13 · 1988 AJHSME
Hard
Geometry & Measurement
circumferenceapproximation
If rose bushes are spaced about 1 foot apart, approximately how many bushes are needed to surround a circular patio whose radius is 12 feet?
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Answer: D — 75.
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Hint 1 of 2
The bushes go *around* the patio, not all over it. So you need the distance around the circle, not how much space it covers.
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Hint 2 of 2
Distance around a circle is its circumference, 2πr. With one bush per foot, the number of bushes ≈ that distance in feet.
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Approach: bushes line the edge, so use circumference = 2πr
- 'Surround' means lining the boundary, so the right measurement is the circumference: 2π · 12 = 24π ≈ 75.4 feet.
- At one bush per foot, about 75 bushes are needed.
- Trap to avoid: choice 450 comes from using area, πr² ≈ 452. But the bushes form a ring around the edge, not a filled-in field — boundary problems use circumference (perimeter), not area.
- Why this transfers: whenever something runs *along the edge* — fencing, lights on a track, bushes around a patio — reach for the perimeter/circumference. 'Covering the inside' is the only time you use area.
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