Geometry and TrigonometryMediumArea of a path around a circular bed
Geometry and Trigonometry practice question
A circular flower bed has an area of 49π square feet. A path of uniform width 1 foot runs around the outside of the bed. What is the area of the path, in square feet?
- A. 15πCorrect
- B. π
- C. 64π
- D. 2π
Answer: A. 15π
The bed's radius is 7 (since πr² = 49π). With the path, the outer radius is 8. Path area = π(8²) − π(7²) = 64π − 49π = 15π.
Why the other answers are wrong
- B. π
- π is the area of a circle of radius 1; the path isn't a small circle but a ring.
- C. 64π
- 64π is the area of the bed AND the path together.
- D. 2π
- 2π is the difference in the two circumferences, not the ring's area.
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