Arc Length – Outschool

ARC LENGTH INSTRUCTION AND QUIZ

Use your skills for finding circumference to find arc length. Here’s how:

Question: In the circle with center K shown below, the length of radius KL is 8 meters. What is the length, in meters, of arc LM?

Step 1: Find the degree measure for the arc.

Because the central angle measures 45^o, the arc also measures 45^o.

Step 2: Find the circumference of the circle.

C = 2πr

C = 16π meters

Step 3: Find the arc length.

Multiply the fraction of the circle in the arc by the circumference of the circle.

Arc length LM = (45/360)• 16π

Arc length LM = (1/8) • 16π

Arc length LM = 2π meters

The length of arc LM is 2π meters, 1/8^th of the full circumference, 16π meters.