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Finding arc length

Arc length is the angle's fraction of 360° times the circumference.

The common mistake

Using the area formula πr² instead of the circumference.

Instead: Arc length = (θ/360) × 2πr.

Worked example with Guide me

Find the arc length for a 90° angle in a circle of radius 8.

  1. Sugar · What fraction of the circle is 90°?
    Student · ¼.
  2. Sugar · Full circumference?
    Student · 16π.
  3. Sugar · A quarter of that?
    Student · 4π.

Answer: 4π ≈ 12.6

Try 3 practice questions

  1. 1. 180°, radius 5?

    Show answer

    5π ≈ 15.7

  2. 2. 60°, radius 6?

    Show answer

    2π ≈ 6.3

  3. 3. 120°, radius 9?

    Show answer

    6π ≈ 18.8

Quick answers

What is the most common mistake with finding arc length?
Using the area formula πr² instead of the circumference.
How do I get finding arc length right?
Arc length = (θ/360) × 2πr.
Can you show a worked example?
Find the arc length for a 90° angle in a circle of radius 8. 4π ≈ 12.6

Related concepts

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