What you’ll learn
Calculate arc length.
Key idea
Arc length is the turn fraction times circumference, not the whole circumference automatically.
Scale circumference by the turn fraction; degrees and boundary length are different quantities.
Worked example
Enter the exact value or ordered values in the format requested below.
A circle of radius 3 cm has minor central angle 170 degrees. Find the exact minor arc length in cm as a multiple of pi, without a unit suffix.
- Circumference=6π cm and turn fraction=170/360=17/36.
- Arc length=17/36*6π=(17/6)π cm.
Answer: (17/6)π
Quick Check
Evaluate a worked attempt at calculate arc length, identify the first invalid step, and provide the correction.
A circle radius is 5 and minor central angle is 100 degrees. Step 1 computes circumference=10π. Step 2 assigns the whole circumference to the minor arc. Locate and repair the first invalid step.