# GMAT Math : Calculating circumference

## Example Questions

### Example Question #1 : Calculating Circumference

A circle on the coordinate plane has equation

Which of the following represents its circumference?

Explanation:

The equation of a circle centered at the origin is

where  is the radius of the circle.

In this equation, , so ; this simplifies to

The circumference of a circle is , so substitute :

### Example Question #2 : Calculating Circumference

A circle on the coordinate plane has equation

What is its circumference?

Explanation:

The standard form of the area of a circle with radius  and center  is

Once we get the equation in standard form, we can find radius , and multiply it by  to get the circumference.

Complete the squares:

so  can be rewritten as follows:

,

so

And

### Example Question #3 : Calculating Circumference

On average, Stephanie walks  feet every  seconds. If Stephanie walks at her usual pace, how long will it take her to walk around a circular track with a radius of  feet, in seconds?

seconds

seconds

seconds

None of the other answers are correct.

seconds

seconds

Explanation:

The length of the track equals the circumference of the circle.

Therefore,  .

### Example Question #4 : Calculating Circumference

A circle on the coordinate plane has equation .

What is its circumference?

Explanation:

The equation of a circle centered at the origin is

,

where  is the radius of the circle.

In the equation given in the question stem, , so .

The circumference of a circle is , so substitute :

### Example Question #5 : Calculating Circumference

Let be concentric circles. Circle has a radius of , and the shortest distance from the edge of circle to the edge of circle is . What is the circumference of circle ?

Explanation:

Since are concentric circles, they share a common center, like sections of a bulls-eye target. Since the radius of is less than half the distance from the edge of to the edge of , we must have circle is inside of circle . (It's helpful to draw a picture to see what's going on!)

Now we can find the radius of by adding and , which is And the equation for finding circumfrence is . Plugging in for gives .

### Example Question #51 : Radius

Consider the Circle :

(Figure not drawn to scale.)

Suppose Circle  represents a circular pen for Frank's mules. How many meters of fencing does Frank need to build this pen?

Explanation:

We need to figure out the length of fencing needed to surround a circular enclosure, or in other words, the circumference of the circle.

Circumference equation:

Where  is our radius, which is  in this case. Plug it in and simplify:

### Example Question #52 : Radius

If the radius of a circle is , what is its circumference?

Explanation:

Using the formula for the circumference of a circle, we can plug in the given value for the radius and calculate our solution:

### Example Question #81 : Geometry

Megan, a civil engineer, is designing a roundabout for the city of Madison. She knows that the distance from the edge of the roundabout to the center must be 25 meters. Help Megan find the circumference of the roundabout.

Explanation:

Megan, a civil engineer, is designing a roundabout for the city of Madison. She knows that the distance from the edge of the roundabout to the center must be 25 meters. Help Megan find the circumference of the roundabout.

We are asked to find circumference. In order to do so, look at the following formula:

Where r is our radius and C is our circumference.

We are indirectly told that our radius is 25 meters, plug it in to get our answer:

### Example Question #82 : Geometry

A circle has radius . Give its circumference.