# Arc Length of a Sector - in Degrees

## Arc Length in Degrees - How it Works - Video

### Example 1 Example 1:

To find the arc length of a circle we need the radius and the central angle. Then we can use the formula, Arc Length = 2πr * θ/360°. Now our first step is substitute the radius and the central into the formula.

So we have arc AB = 2π(8) * (60°)/360°.

Next multiply the numbers next to pi ==> 16π * (60°)/360°.

Now we simplify the 60 and the 360 by dividing each number by 60° ==> 16π * 1/6.

Next we multiply the two numbers 16 and 1/6 ==> 16/6*π.

Now we simplify the 16 and 6 by dividing each number by 2 ==> 8/3*π cm. And that is the final simplified version. Sometimes the answer needs to be in decimal so we multiply 8/3 and π ==> 8.38 cm is another possible result.

### Example 2 Example 2:

To find the arc length of a circle we need the radius and the central angle. Then we can use the formula, Arc Length = 2πr * θ/360°. Now our first step is substitute the radius and the central into the formula.

So we have arc AB = 2π(12) * (150°)/360°.

Next multiply the numbers next to pi ==> 24π * (150°)/360°.

Now we simplify the 150 and the 360 by dividing each number by 30° ==> 24π * 5/12.

Next we multiply the two numbers 24 and 5/12 ==> 120/12*π.

Now we simplify the 120 and 12 by dividing each number by 12 ==> 10*π m. And that is the final simplified version. Sometimes the answer needs to be in decimal so we multiple 10 and π ==> 31.42 m is another possible result.

### Example 3  Example 3a:

To find the arc length of a circle we need the radius and the central angle. Then we can use the formula, Arc Length = 2πr * θ/360°. Now our first step is substitute the radius and the central into the formula.

So we have arc MNO = 2π(10) * (225°)/360°.

Next multiply the numbers next to pi ==> 20π * (225°)/360°.

Now we simplify the 225 and the 360 by dividing each number by 45° ==> 20π * 5/8.

Next we multiply the two numbers 20 and 5/8 ==> 100/8*π.

Now we simplify the 100 and 8 by dividing each number by 4 ==> 25/2*π cm. And that is the final simplified version. Sometimes the answer needs to be in decimal so we multiple 25/2 and π ==> 39.27 cm is another possible result.

Example 3b:

To find the arc length of a circle we need the radius and the central angle. Then we can use the formula, Arc Length = 2πr * θ/360°. Now our first step is substitute the radius and the central into the formula.

So we have arc MO = 2π(10) * (135°)/360°.

Next multiply the numbers next to pi ==> 20π * (135°)/360°.

Now we simplify the 135 and the 360 by dividing each number by 45° ==> 20π * 3/8.

Next we multiply the two numbers 20 and 3/8 ==> 60/8*π.

Now we simplify the 60 and 8 by dividing each number by 4 ==> 15/2*π cm. And that is the final simplified version. Sometimes the answer needs to be in decimal so we multiple 15/2 and π ==> 23.56 cm is another possible result.