GRE Math : How to find circumference

Study concepts, example questions & explanations for GRE Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : Geometry

What is the circumference of a circle with an area of 36π?

Possible Answers:

None of the other answers

32

12π

15π

Correct answer:

12π

Explanation:

We know that the area of a circle can be expressed: a = πr2

If we know that the area is 36π, we can substitute this into said equation and get: 36π = πr2

Solving for r, we get: 36 = r2; (after taking the square root of both sides:) 6 = r

Now, we know that the circuference of a circle is expressed: c = πd.  Since we know that d = 2r (two radii, placed one after the other, make a diameter), we can rewrite the circumference equation to be: c = 2πr

Since we have r, we can rewrite this to be: c = 2π*6 = 12π

Example Question #1 : Circles

Which is greater: the circumference of a circle with an area of , or the perimeter of a square with side length  inches?

 

 

 

 

Possible Answers:

The circumference of the circle is greater.

The perimeter of the square is greater.

The relationship cannot be determined from the information given.

The two quantities are equal.

Correct answer:

The circumference of the circle is greater.

Explanation:

Starting with the circle, we need to find the radius in order to get the circumference. Find \dpi{100} \small r by plugging our given area into the equation for the area of a circle:

A = \pi r^2

25\pi = \pi r^2

25 = r^2

Then calculate circumference:

C = 2\pi r

\dpi{100} \small C = 2\pi \times 5 = 10\pi \approx 31.4 inches (approximating \dpi{100} \small \pi as 3.14)

To find the perimeter of the square, we can use P = 4s , where \dpi{100} \small P is the perimeter and \dpi{100} \small s is the side length:

\dpi{100} \small 31.4>28, so the circle's circumference is greater.

Example Question #2 : Circles

Circle A has an area of .  What is the perimeter of an enclosed semi-circle with half the radius of circle A?

Possible Answers:

 

Correct answer:

Explanation:

Based on our information, we know that the 121π = πr2; 121 = r2; r = 11.

Our other circle with half the radius of A has a diameter equal to the radius of A.  Therefore, the circumference of this circle is 11π.  Half of this is 5.5π.  However, since this is a semi circle, it is enclosed and looks like this:

Semicircle

Therefore, we have to include the diameter in the perimeter.  Therefore, the total perimeter of the semi-circle is 5.5π + 11.

Example Question #4 : Radius

Quantity A: The circumference of a circle with radius 

Quantity B: The area of a circle with a diameter one fourth the radius of the circle in Quantity A 

Which of the following is true?

Possible Answers:

The two quantities are equal.

Quantity B is larger.

The relationship between the two values cannot be determined.

Quantity A is larger.

Correct answer:

The relationship between the two values cannot be determined.

Explanation:

Let's compute each value separately. We know that the radii are positive numbers that are greater than or equal to . This means that we do not need to worry about the fact that the area could represent a square of a decimal value like .

Quantity A

Since , we know:

Quantity B

If the diameter is one-fourth the radius of A, we know:

Thus, the radius must be half of that, or .

Now, we need to compute the area of this circle. We know:

Therefore, 

Now, notice that if , Quantity A is larger.

However, if we choose a value like , we have:

Quantity A: 

Quantity B: 

Therefore, the relation cannot be determined!

Example Question #4 : Plane Geometry

Inscribedsquare

Circle  has a center in the center of Square .

The area of Square  is  .

What is the circumference of Circle ?

Possible Answers:

 

 

 

 

 

Correct answer:

 

Explanation:

Since we know that the area of Square  is , we know , where  is the length of one of its sides. From this, we can solve for  by taking the square root of both sides. You will have to do this by estimating upward. Therefore, you know that  is . By careful guessing, you can quickly see that  is . From this, you know that the diameter of your circle must be half of , or  (because it is circumscribed). Therefore, you can draw:

Inscribedsquare24

The circumference of this circle is defined as:

 or, for your values:

(You could also compute this from the diameter, but many students just memorize the formula above.)

Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: