### All GMAT Math Resources

## Example Questions

### Example Question #41 : Radius

A arc of a circle measures . Give the radius of this circle.

**Possible Answers:**

**Correct answer:**

A arc of a circle is of the circle. Since the length of this arc is , the circumference is this, or

The radius of a circle is its circumference divided by ; therefore, the radius is

### Example Question #42 : Radius

The arc of a circle measures . The chord of the arc, , has length . Give the length of the radius of the circle.

**Possible Answers:**

**Correct answer:**

A circle can be divided into congruent arcs that measure

.

If the (congruent) chords are constructed, the figure will be a regular hexagon. The radius of this hexagon will be equal to the length of one side - one chord of the circle; this radius will coincide with the radius of the circle. Therefore, the radius of the circle is the length of chord , or .

### Example Question #12 : Calculating The Length Of A Radius

If a monster truck's wheels have circumference of , what is the distance from the ground to the center of the wheel?

**Possible Answers:**

**Correct answer:**

If a monster truck's wheels have circumference of , what is the distance from the ground to the center of the wheel?

This question is asking us to find the radius of a circle. the distance from the outside of the circle to the center is the radius. We are given the circumference, so use the following formula:

Then, plug in what we know and solve for r

### Example Question #44 : Radius

Two circles in the same plane have the same center. The smaller circle has radius 10; the area of the region between the circles is . What is the radius of the larger circle?

**Possible Answers:**

**Correct answer:**

The area of a circle with radius is .

Let be the radius of the larger circle. Its area is . The area of the smaller circle is . Since the area of the region between the circles is , and is the difference of these areas, we have

The smaller circle has radius .

### Example Question #311 : Gmat Quantitative Reasoning

A circle on the coordinate plane has equation

Which of the following represents its circumference?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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 #41 : Radius

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?

**Possible Answers:**

None of the other answers are correct.

seconds

seconds

seconds

seconds

**Correct answer:**

seconds

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

Therefore, .

### Example Question #2 : Calculating Circumference

A circle on the coordinate plane has equation .

What is its circumference?

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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:

And we have our answer!

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