GMAT Math : Geometry

Study concepts, example questions & explanations for GMAT Math

Create An Account

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #13 : Calculating The Length Of A Radius

A $60^{\circ }$ arc of a circle measures x+ 4 . Give the radius of this circle.

Possible Answers:

$\frac{6}{\pi}x+\frac{24}{\pi}$

$9 \pi x^{2}+ 72 \pi x+ 144 \pi$

$6 \pi x+24 \pi$

$\frac{3}{\pi}x+\frac{12}{\pi}$

$3\pi x+12\pi$

Correct answer:

$\frac{3}{\pi}x+\frac{12}{\pi}$

Explanation:

A $60^{\circ }$ arc of a circle is $\frac{60}{360 } = \frac{1}{6}$ of the circle. Since the length of this arc is x+ 4 , the circumference is $\textup{six times }$ this, or

C = 6( x+ 4) = 6x+ 24

The radius of a circle is its circumference divided by $2 \pi$ ; therefore, the radius is

$r = \frac{C}{2 \pi} = \frac{6x+24}{2\pi} = \frac{3}{\pi}x+\frac{12}{\pi}$

Report an Error

Example Question #14 : Calculating The Length Of A Radius

The arc $\widehat{AB}$ of a circle measures $60^{\circ }$ . The chord of the arc, $\overline{AB}$ , has length x + 2 . Give the length of the radius of the circle.

Possible Answers:

x+2

$2 \pi x + 4 \pi$

2x+4

$\textup{None of the other responses gives a correct answer.}$

$\pi x +2 \pi$

Correct answer:

x+2

Explanation:

A circle can be divided into congruent arcs that measure

$\frac{1}{6} \cdot 360 ^{\circ } = 60 ^{\circ }$ .

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 $60 ^{\circ }$ 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 $\overline{AB}$ , or x+2 .

Report an Error

Example Question #15 : 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:

3ft

2.5ft

5ft

10ft

Correct answer:

5ft

Explanation:

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:

$Circ=2 \pi r$

Then, plug in what we know and solve for r

$31.4=2 \pi r$

$r=\frac{31.4}{2 \pi}=4.997\approx5ft$

Report an Error

Example Question #311 : Gmat Quantitative Reasoning

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 $50 \pi$ . What is the radius of the larger circle?

Possible Answers:

$5 \sqrt{2}$

$6 \sqrt{5}$

$5 \sqrt{6}$

Correct answer:

$5 \sqrt{6}$

Explanation:

The area of a circle with radius is $A = \pi r^{2}$ .

Let be the radius of the larger circle. Its area is $A_{1} = \pi R^{2}$ . The area of the smaller circle is $A_{2} = \pi \cdot 10^{2} = 100 \pi$ . Since the area of the region between the circles is $50 \pi$ , and is the difference of these areas, we have

$\pi R^{2} - 100 \pi = 50 \pi$

$\pi R^{2} - 100 \pi+ 100 \pi = 50 \pi + 100 \pi$

$\pi R^{2} = 150 \pi$

$R^{2} = 150$

$R = \sqrt{150} = \sqrt {25 } \cdot \sqrt{6} = 5 \sqrt{6}$

The smaller circle has radius $5 \sqrt{6}$ .

Report an Error

Example Question #1 : Calculating Circumference

A circle on the coordinate plane has equation

$x^{2} + y ^{2} = 40$

Which of the following represents its circumference?

Possible Answers:

$80 \pi$

$16 \pi \sqrt{10}$

$4 \pi \sqrt{10}$

$40 \pi$

$8 \pi \sqrt{10}$

Correct answer:

$4 \pi \sqrt{10}$

Explanation:

The equation of a circle centered at the origin is

$x^{2} + y ^{2} = r ^{2}$

where is the radius of the circle.

In this equation, $r ^{2} = 40$ , so $r = \sqrt{40}$ ; this simplifies to

$r = \sqrt{40} = \sqrt{4} \cdot \sqrt{10} = 2 \sqrt{10}$

The circumference of a circle is $C = 2 \pi r$ , so substitute $r = 2 \sqrt{10}$ :

$C = 2 \pi r = 2 \pi \cdot 2 \sqrt{10} = 4 \pi \sqrt{10}$

Report an Error

Example Question #1 : Calculating Circumference

A circle on the coordinate plane has equation

$x ^{2} - 8x + y ^{2} - 10x = 7$

What is its circumference?

Possible Answers:

$4 \pi \sqrt{ 3}$

$48 \pi$

$16 \pi \sqrt{ 3}$

$8 \pi \sqrt{ 3}$

$96 \pi$

Correct answer:

$8 \pi \sqrt{ 3}$

Explanation:

The standard form of the area of a circle with radius and center (h,k ) is

$(x-h)^{2} + (y-k)^{2} = r^{2}$

Once we get the equation in standard form, we can find radius , and multiply it by $2 \pi$ to get the circumference.

Complete the squares:

$\left (\frac{-8}{2} \right )^{2} = 16,\left (\frac{-10}{2} \right )^{2} = 25$

so $x ^{2} - 8x + y ^{2} - 10x = 7$ can be rewritten as follows:

$x ^{2} - 8x + 16 + y ^{2} - 10x + 25 = 7 + 16 + 25$

$\left ( x -4 \right )^{2} + \left ( y -5 \right ) ^{2} = 48$

$r ^{2} = 48$ ,

so $r = \sqrt{48} = \sqrt{16} \cdot \sqrt{3} = 4 \sqrt{3}$

And $C = 2\pi \cdot 4 \sqrt{ 3} = 8 \pi \sqrt{ 3}$

Report an Error

Example Question #71 : Geometry

On average, Stephanie walks $2\pi$ 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 200 feet, in seconds?

Possible Answers:

None of the other answers are correct.

400 seconds

800 seconds

$800 \pi$ seconds

$400 \pi$ seconds

Correct answer:

800 seconds

Explanation:

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

$C = 2\pi r$

$C=2\pi (200)=400\pi$

$Speed = \frac{distance}{time}$

Therefore, $time = \frac{distance}{speed}$ .

$time = 400\pi\: ft \div \frac{2\pi \: ft}{4\: sec} = 400\pi\: ft \times\frac{4\:sec}{2\pi\: feet}$

$time= 400\pi\: ft \times\frac{2\:sec}{1\pi\: feet} = 800\:seconds$

Report an Error

Example Question #72 : Geometry

A circle on the coordinate plane has equation $x^{2} + y ^{2} = 64$ .

What is its circumference?

Possible Answers:

$8 \pi$

$64 \pi$

$16 \pi ^2$

$8 \pi ^2$

$16 \pi$

Correct answer:

$16 \pi$

Explanation:

The equation of a circle centered at the origin is

$x^{2} + y ^{2} = r ^{2}$ ,

where is the radius of the circle.

In the equation given in the question stem, $r ^{2} = 64$ , so $r = \sqrt{64} = 8$ .

The circumference of a circle is $C = 2 \pi r$ , so substitute r = 8 :

$C = 2 \pi r = 2 \pi \cdot 8 = 16 \pi$

Report an Error

Example Question #2 : Calculating Circumference

Let A, B 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:

$10\pi$

$6\pi$

$40\pi$

$\pi$

$14\pi$

Correct answer:

$40\pi$

Explanation:

Since A,B 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 20. And the equation for finding circumfrence is $C =2r\pi$ . Plugging in for gives $40\pi$ .

Report an Error

Example Question #2 : Calculating Circumference

Consider the Circle :

Circle3

(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:

$60 \pi\:m$

$45 \pi\:m$

$30 \pi\:m$

$225 \pi\:m$

$15 \pi\:m$

Correct answer:

$30 \pi\:m$

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:

$C=2 \pi r$

Where is our radius, which is $15\:m$ in this case. Plug it in and simplify:

$C=2 \pi *15=30 \pi\:m$

And we have our answer!

Report an Error

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Biology Tutors in Los Angeles, Statistics Tutors in Boston, ACT Tutors in Seattle, Biology Tutors in Washington DC, ACT Tutors in Philadelphia, Physics Tutors in Boston, Computer Science Tutors in Atlanta, Statistics Tutors in Washington DC, Algebra Tutors in New York City, Chemistry Tutors in Miami

Popular Courses & Classes

GMAT Courses & Classes in Seattle, ACT Courses & Classes in Seattle, SSAT Courses & Classes in Houston, MCAT Courses & Classes in Houston, ISEE Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Philadelphia, SSAT Courses & Classes in New York City, ACT Courses & Classes in Philadelphia, GMAT Courses & Classes in Denver

Popular Test Prep

ACT Test Prep in Dallas Fort Worth, GRE Test Prep in Washington DC, GRE Test Prep in Dallas Fort Worth, SAT Test Prep in San Francisco-Bay Area, GRE Test Prep in San Francisco-Bay Area, ACT Test Prep in Philadelphia, SSAT Test Prep in Atlanta, ISEE Test Prep in Denver, GMAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Houston

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

Email address:
Your name:
Feedback:

GMAT Math : Geometry

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #13 : Calculating The Length Of A Radius

Example Question #14 : Calculating The Length Of A Radius

Example Question #15 : Calculating The Length Of A Radius

Example Question #311 : Gmat Quantitative Reasoning

Example Question #1 : Calculating Circumference

Example Question #1 : Calculating Circumference

Example Question #71 : Geometry

Example Question #72 : Geometry

Example Question #2 : Calculating Circumference

Example Question #2 : Calculating Circumference

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details