# Intermediate Geometry : How to find the length of an arc

## Example Questions

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### Example Question #71 : Circles

If the area of a circle is 1.44, what is its circumference?

Explanation:

Utilizing the formula for area of a circle , you would plug in the answer for area as

=

Divide both sides by

Then square root both sides to get

Then plug in 1.2 for  in the equation for circumference for a circle,  .   Thus

### Example Question #1 : How To Find The Length Of An Arc

In the circle above, the angle A in radians is

What is the length of arc A?

Explanation:

Circumference of a Circle =

Arc Length

### Example Question #2 : How To Find The Length Of An Arc

A sector of a circle with radius of  feet has an area of  square feet.  Find the length of the arc of the sector.

Explanation:

We begin with the formula for the area of a sector

where  is the measure of the central angle in degrees and  is the radius.

Substituting what we know gives

Therefore our central angle is

We then turn to our formula for arc length.

Substituting gives

Therefore, our arc length is

### Example Question #1 : How To Find The Length Of An Arc

Find the perimeter around the following semicircle.

Explanation:

First, you would need to find the radius of the semi-circle.  18 divided by 2 results in 9 cm for the radius.  Then you would take the formula for finding circumference   and plug in  to get

.

Then you would divide that result by 2 to get  since it is a semicircle.  Lastly you would add 18 cm to  because the perimeter is the sum of the semicircle and the diameter.  Remember that they are not like terms.

If you chose , you forgot to include the diameter.

If you chose , you added  and , but they are not like terms.

If you chose , remember that you only need half of the circumference.

### Example Question #4 : How To Find The Length Of An Arc

The radius of a circle is . Find the length of an arc if it has a measure of  degrees.

Explanation:

Recall that the length of an arc is merely a part of the circle's circumference.

We can then write the following equation to find the length of an arc:

Plug in the values of the arc angle measure and the radius to find the length of the arc.

### Example Question #5 : How To Find The Length Of An Arc

The radius of a circle is . Find the length of an arc if it has a measurement of  degrees.

Explanation:

Recall that the length of an arc is merely a part of the circle's circumference.

We can then write the following equation to find the length of an arc:

Plug in the values of the arc angle measure and the radius to find the length of the arc.

### Example Question #6 : How To Find The Length Of An Arc

The radius of a circle is . Find the length of an arc that has a measurement of  degrees.

Explanation:

Recall that the length of an arc is merely a part of the circle's circumference.

We can then write the following equation to find the length of an arc:

Plug in the values of the arc angle measure and the radius to find the length of the arc.

### Example Question #7 : How To Find The Length Of An Arc

The radius of a circle is . Find the length of an arc if it has a measure of  degrees.

Explanation:

Recall that the length of an arc is merely a part of the circle's circumference.

We can then write the following equation to find the length of an arc:

Plug in the values of the arc angle measure and the radius to find the length of the arc.

### Example Question #8 : How To Find The Length Of An Arc

The radius of a circle is . Find the length of an arc that has a measure of  degrees.

Explanation:

Recall that the length of an arc is merely a part of the circle's circumference.

We can then write the following equation to find the length of an arc:

Plug in the values of the arc angle measure and the radius to find the length of the arc.

### Example Question #9 : How To Find The Length Of An Arc

The radius of a circle is . Find the length of an arc if it has a measure of  degrees.