Practice Arc Length in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The distance along a portion of a circle's circumference, determined by the central angle and the radius.
Imagine walking along a circular track but only covering a portion of the full loop. The arc length is how far you actually walked. If you walk a quarter of the circle (90°), you cover a quarter of the circumference. The fraction of the full circle you cover determines the fraction of the circumference you walk.
Example 1
easyA circle has radius 6 cm. Find the arc length intercepted by a central angle of 60°.
Example 2
mediumA circle has radius 5 m. Find the arc length subtended by a central angle of \frac{3\pi}{4} radians.
Example 3
easyA circle has a radius of 10 cm. What is the arc length for a central angle of 90°?
Example 4
hardA pendulum of length 80 cm swings through an angle of 0.4 radians. How far does the tip of the pendulum travel in one complete swing (from one side to the other and back)?