What if you were given the angle measure of a circle's arc? How could you find the length of that arc? After completing this Concept, you'll be able to find an arc's length, or its portion of a circle's circumference.

### Watch This

### Guidance

One way to measure arcs is in degrees. This is called the “arc measure” or “degree measure” (see Arcs in Circles). Arcs can also be measured in length, as a portion of the circumference. **Arc length** is the length of an arc or a portion of a circle’s circumference. The arc length is directly related to the degree arc measure.

**Arc Length Formula:** The length of or .

#### Example A

Find the length of . Leave your answer in terms of .

In the picture, the central angle that corresponds with is . This means that . Think of the arc length as a portion of the circumference. There are in a circle, so would be of that . Therefore, the length of is of the circumference. *length of* units.

#### Example B

The arc length of a circle is and is the circumference. Find the radius of the circle.

If is the circumference, then the total circumference is . To find the radius, plug this into the circumference formula and solve for .

#### Example C

Find the measure of the central angle or .

Let’s plug in what we know to the Arc Length Formula.

-->

### Guided Practice

Find the arc length of in . Leave your answers in terms of .

1.

2.

3. A typical large pizza has a diameter of 14 inches and is cut into 8 pieces. Think of the crust as the circumference of the pizza. Find the *length* of the crust for the entire pizza. Then, find the length of the crust for one piece of pizza if the entire pizza is cut into 8 pieces.

**Answers:**

1. Use the Arc Length formula.

2. Use the Arc Length formula.

3. The entire length of the crust, or the circumference of the pizza, is . In of the pizza, one piece would have inches of crust.

### Explore More

Find the arc length of in . Leave your answers in terms of .

Find (the radius) in . Leave your answer in terms of .

Find the central angle or in . Round any decimal answers to the nearest tenth.

### Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 10.9.