Arc Length Math Example 3

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

easy

A circle has a radius of

10

cm. What is the arc length for a central angle of

90°

1
Step 1: Use $s = \frac{\theta}{360°} \times 2\pi r = \frac{90}{360} \times 2\pi(10) = \frac{1}{4} \times 20\pi$ .
2
Step 2: Simplify: $s = 5\pi \approx 15.71$ cm.

Answer

s = 5\pi \approx 15.71

A 90° central angle is one-quarter of a full circle (360°). One-quarter of the full circumference

20\pi

cm gives an arc length of

5\pi

cm.

About Arc Length

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

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