Geometry and TrigonometryVery hardArea of a sector
Geometry and Trigonometry practice question
A circle has radius 9. What is the area of the sector formed by a central angle of 40°?
- A. 9πCorrect
- B. 81π
- C. 2π
- D. 18π
Answer: A. 9π
The whole circle's area is π(9)² = 81π. A 40° sector is 40/360 = 1/9 of the circle, so its area is (1/9)(81π) = 9π.
Why the other answers are wrong
- B. 81π
- 81π is the area of the ENTIRE circle. The sector is only the 40° slice — one ninth of it.
- C. 2π
- 2π is the ARC LENGTH of the sector: (1/9)(18π). The question asks for the area, which uses πr², not 2πr.
- D. 18π
- 18π is the circumference of the circle, 2π(9). Sector area starts from πr² = 81π, then takes the 40° fraction.
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