Arc Length Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
A circle has radius 66 cm. Find the arc length intercepted by a central angle of 60°60°.

Solution

  1. 1
    Step 1: Write the arc length formula using degrees: s=θ360°×2πrs = \frac{\theta}{360°} \times 2\pi r.
  2. 2
    Step 2: Substitute θ=60°\theta = 60° and r=6r = 6 cm: s=60360×2π(6)s = \frac{60}{360} \times 2\pi(6).
  3. 3
    Step 3: Simplify the fraction: 60360=16\frac{60}{360} = \frac{1}{6}, so s=16×12πs = \frac{1}{6} \times 12\pi.
  4. 4
    Step 4: Compute: s=2π≈6.28s = 2\pi \approx 6.28 cm.

Answer

s=2π≈6.28s = 2\pi \approx 6.28 cm
Arc length is the fraction of the full circumference determined by the central angle. A 60° angle is one-sixth of 360°, so the arc is one-sixth of the full circumference 2π(6)=12π2\pi(6) = 12\pi, giving 2π2\pi cm.

About Arc Length

The distance along a portion of a circle's circumference, determined by the central angle and the radius.

Learn more about Arc Length →

More Arc Length Examples

Example 2 medium

A circle has radius [formula] m. Find the arc length subtended by a central angle of [formula] radia

Example 3 easy

A circle has a radius of [formula] cm. What is the arc length for a central angle of [formula]?

Example 4 hard

A pendulum of length [formula] cm swings through an angle of [formula] radians. How far does the tip

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