Geometry and TrigonometryHardArea between two concentric circles
Geometry and Trigonometry practice question
Two circles share the same centre. One has a radius of 3 and the other a radius of 5. What is the area of the ring-shaped region between them?
- A. 16πCorrect
- B. 4π
- C. 34π
- D. 2π
Answer: A. 16π
Outer area π(5²) = 25π, inner area π(3²) = 9π. Ring: 25π − 9π = 16π.
Why the other answers are wrong
- B. 4π
- 4π is π(5 − 3)², squaring the difference of the radii instead of subtracting the squares.
- C. 34π
- 34π ADDS the two areas.
- D. 2π
- 2π uses the difference of the radii, 2, without squaring.
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