Geometry and TrigonometryHardCentral angle from a sector's area
Geometry and Trigonometry practice question
A sector of a circle with radius 6 has an area of 12π. What is the measure, in degrees, of the sector's central angle?
Answer: 120
The whole circle has area π(6²) = 36π. The sector is 12π/36π = 1/3 of the circle, so its angle is (1/3)(360) = 120°.
Common wrong answers
- If you answered 60
- 60 would be a sixth of the circle, an area of 6π.
- If you answered 90
- 90 would be a quarter of the circle, an area of 9π.
- If you answered 240
- 240 is two-thirds of the circle, twice the sector's share.
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What is the measure, in degrees, of the central angle of this sector?
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