Geometry and TrigonometryHardArc length from a central angle
Geometry and Trigonometry practice question
A circle has radius 6. What is the length of the arc intercepted by a central angle of 60°?
- A. 2πCorrect
- B. 6π
- C. 12π
- D. π
Answer: A. 2π
The whole circumference is 2π(6) = 12π. A 60° central angle is 60/360 = 1/6 of the circle, so the arc is (1/6)(12π) = 2π.
Why the other answers are wrong
- B. 6π
- 6π is half the circumference, which would be a 180° arc. 60° is only one sixth.
- C. 12π
- 12π is the entire circumference — the full 360°. The arc is just the 60° part.
- D. π
- π is 1/12 of the circumference, which would be a 30° arc. 60/360 is 1/6, not 1/12.
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