Geometry and TrigonometryMediumSector area from the circle's area
Geometry and Trigonometry practice question
A circle has an area of 36π. What is the area of a sector of the circle with a central angle of 90°?
- A. 9πCorrect
- B. 6π
- C. 18π
- D. 3π
Answer: A. 9π
A 90° angle is 90/360 = 1/4 of the circle, so the sector has 1/4 of the area: 36π/4 = 9π.
Why the other answers are wrong
- B. 6π
- 6π uses the radius (√36 = 6) as if it were the answer. The sector is a quarter of the AREA.
- C. 18π
- 18π is half the circle, which would need a 180° angle.
- D. 3π
- 3π is 36π/12, using 90/1080 or a similar slip; 90/360 = 1/4.
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