Geometry and TrigonometryEasy–MediumArc length from circumference
Geometry and Trigonometry practice question
A circle has a circumference of 24. An arc of the circle is intercepted by a central angle of 60°. What is the length of the arc?
Answer: 4
A 60° central angle is 60/360 = 1/6 of the full circle, so the arc is 1/6 of the circumference: 24/6 = 4.
Common wrong answers
- If you answered 6
- 6 is 24/4, using 90° as the fraction (1/4). The angle is 60°, which is 1/6 of 360°.
- If you answered 8
- 8 is 24/3, treating 60° as 1/3 of the circle. 60/360 = 1/6.
- If you answered 10
- 10 is 24 × 60/144 or some other slip. Arc = (60/360) × 24 = 4.
More Geometry and Trigonometry questions
- Easy–Medium
A circle has a radius of 6. What is its area? (Use A = πr².) - Easy–Medium
A right triangle has legs of length 6 and 8. What is the length of the hypotenuse? - Easy–Medium
A circle has a radius of 5. What is its circumference? (Use C = 2πr.) - Easy–Medium
What is the midpoint of the segment joining the points (2, 3) and (8, 11)? - Easy–Medium
What is the measure, in degrees, of angle B? - Easy–Medium
What is the area, in square centimeters, of the trapezoid?
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