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 #2 : Calculating The Length Of A Radius

The points L (-4,5) and K (9,3) form a line which passes through the center of circle Q. Both points are on circle Q.

To the nearest hundreth, what is the length of the radius of circle Q?

Possible Answers:

15.00

13.15

6.58

13.2

6.6

Correct answer:

6.58

Explanation:

To begin this problem, we need to recognize that the distance between points L and K is our diameter. Segment LK passes from one point on circle Q through the center, to another point on circle Q. Sounds like a diameter to me! Use distance formula to find the length of LK.

$d=\sqrt{(x-x')^2+(y-y')^2}$

Plug in our points and simplify:

$d=\sqrt{(9--4)^2+(3-5)^2}=\sqrt{13^2+2^2}=\sqrt{173}\approx13.15$

Now, don't be fooled into choosing 13.15. That is our diameter, so our radius will be half of 13.15, or 6.575. This rounds to 6.58

Report an Error

Example Question #3 : Calculating The Length Of A Radius

If the trunk of a particular tree is $34\pi$ feet around at chest height, what is the radius of the tree at the same height?

Possible Answers:

96 ft

17 ft

45 ft

8.5 ft

34 ft

Correct answer:

17 ft

Explanation:

A close reading of the question reveals that we are given the circumference and asked to find the radius.

Circumference formula:

$C=2 \pi r$

So,

$34 \pi=2 \pi r$

$r=34\pi\div2 \pi=17$

So 17 feet

Report an Error

Example Question #4 : Calculating The Length Of A Radius

If the circumference of a circle is $42\pi$ , what is its radius?

Possible Answers:

Correct answer:

Explanation:

Using the formula for the circumference of a circle, we can solve for its radius. Plugging in the given value for the circumference, we have:

$C=2\pi r$

$42\pi=2\pi r$

$r=\frac{42\pi }{2\pi }=21$

Report an Error

Example Question #31 : Radius

If the area of a circle is $25\pi$ , what is its radius?

Possible Answers:

Correct answer:

Explanation:

Using the formula for the area of a circle, we can solve for its radius. Plugging in the given value for the area of the circle, we have:

$A=\pi r^2$

$25\pi=\pi r^2$

r^2=25

r=5

Report an Error

Example Question #1 : Calculating The Length Of A Radius

Given that the area of a circle is $64\pi$ , determine the radius.

Possible Answers:

$8\pi$

$16\pi$

Correct answer:

Explanation:

To solve, use the formula for the area of a circle, $A={\pi}r^2$ , and solve for .

$64\pi=\pi{r^2}\Rightarrow 64=r^2\Rightarrow r=8$

Report an Error

Example Question #7 : Calculating The Length Of A Radius

Given a circumferene of $42 \pi$ , find the circle's radius.

Possible Answers:

6.48

$21\pi$

Correct answer:

Explanation:

The circumference of a circle, in terms of radius, can be found by: $C=2r \pi$

We are told the circumference with respect to $\pi$ so we can easily solve for the radius:

$42 \pi = 2 r \pi$

Notice how the $\pi$ cancels out

42 = 2r

r=21

Report an Error

Example Question #2 : Calculating The Length Of A Radius

The circumference of a circle measures $27\pi$ . Find the radius.

Possible Answers:

8.6

5.2

13.5

Correct answer:

13.5

Explanation:

Solving this problem is rather straightforward, we just need to remember the circumference of circle is found by $C=2r\pi$ and in this case, we're given the circumference in terms of $\pi$ .

$27\pi = 2 r \pi$

Notice how the $\pi$ cancel out

27=2r

r=13.5

Report an Error

Example Question #9 : Calculating The Length Of A Radius

The arc $\widehat{AB}$ of a circle measures $120^{\circ }$ . The chord of the arc, $\overline{AB}$ , has length x + 2 . Give the length of the radius of the circle.

Possible Answers:

x + 2

$\frac{\sqrt{3}}{6} x+ \frac{ \sqrt{3}}{3}$

$\frac{\sqrt{3}}{4} x+ \frac{ \sqrt{3}}{2}$

$\frac{\sqrt{3}}{12} x+ \frac{ \sqrt{3}}{6}$

$x \sqrt{3} + 2 \sqrt{3}$

Correct answer:

$\frac{\sqrt{3}}{6} x+ \frac{ \sqrt{3}}{3}$

Explanation:

A circle can be divided into three congruent arcs that measure

$\frac{1}{3} \cdot 360 ^{\circ } = 120 ^{\circ }$ .

If the three (congruent) chords are constructed, the figure will be an equilateral triangle. The figure is below, along with the altitudes of the triangle:

Circle and triangle

Since AB = x + 2 , it follows by way of the 30-60-90 Triangle Theorem that

$BM = \frac{1}{2} AB = \frac{1}{2} (x+2) = \frac{1}{2} x+1$

and

$AM = \frac{ \sqrt{3}}{2} \cdot BM = \frac{ \sqrt{3}}{2} \cdot \left ( \frac{1}{2} x+1 \right ) = \frac{\sqrt{3}}{4} x+ \frac{ \sqrt{3}}{2}$

The three altitudes of an equilateral triangle split each other into segments that have ratio 2:1. Therefore,

$OA = \frac{2}{3} \cdot AM$

$=\frac{2}{3} \cdot \left ( \frac{\sqrt{3}}{4} x+ \frac{ \sqrt{3}}{2} \right )$

$= \frac{\sqrt{3}}{6} x+ \frac{ \sqrt{3}}{3}$

Report an Error

Example Question #11 : Calculating The Length Of A Radius

The arc $\widehat{AB}$ of a circle measures $90^{\circ }$ . The chord of the arc, $\overline{AB}$ , has length x + 2 . Give the radius of the circle.

Possible Answers:

2x+4

$\pi x+ 2 \pi$

$x \sqrt{2} + 2 \sqrt{2}$

$2 \pi x+ 4 \pi$

$\frac{1}{2} x \sqrt{2} + \sqrt{2}$

Correct answer:

$\frac{1}{2} x \sqrt{2} + \sqrt{2}$

Explanation:

A circle can be divided into four congruent arcs that measure

$\frac{1}{4} \cdot 360 ^{\circ } = 90 ^{\circ }$ .

If the four (congruent) chords of the arcs are constructed, they will form a square with sides of length x + 2 . The diagonal of a square has length $\sqrt{2}$ times that of a side, which will be

$(x + 2) \sqrt{2} = x \sqrt{2} + 2 \sqrt{2}$

A diagonal of the square is also a diameter of the circle; the circle will have radius half this length, or

$\frac{1}{2} \left ( x \sqrt{2} + 2 \sqrt{2} \right ) =\frac{1}{2} x \sqrt{2} + \sqrt{2}$

Report an Error

Example Question #301 : Problem Solving Questions

Two circles in the same plane have the same center. The larger circle has radius 10; the area of the region between the circles is $50 \pi$ . What is the radius of the smaller circle?

Possible Answers:

$5 \sqrt{6}$

$5 \sqrt{2}$

$10 \sqrt{2}$

Correct answer:

$5 \sqrt{2}$

Explanation:

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

Let be the radius of the smaller circle. Its area is $A_{1} = \pi R^{2}$ . The area of the larger 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

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

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

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

$R^{2} = 50$

$R = \sqrt{50} = \sqrt {25 } \cdot \sqrt{2} = 5 \sqrt{2}$

The smaller circle has radius $5 \sqrt{2}$ .

Report an Error

All GMAT Math Resources

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

Popular Subjects

ACT Tutors in Seattle, English Tutors in New York City, Reading Tutors in San Francisco-Bay Area, GRE Tutors in Dallas Fort Worth, Math Tutors in Houston, Spanish Tutors in Phoenix, MCAT Tutors in Boston, Statistics Tutors in Los Angeles, Computer Science Tutors in Los Angeles, Biology Tutors in Denver

Popular Courses & Classes

GMAT Courses & Classes in New York City, LSAT Courses & Classes in Los Angeles, Spanish Courses & Classes in Washington DC, Spanish Courses & Classes in Boston, ACT Courses & Classes in Atlanta, MCAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Atlanta, SSAT Courses & Classes in Seattle, ACT Courses & Classes in Miami, Spanish Courses & Classes in Phoenix

Popular Test Prep

SAT Test Prep in Philadelphia, SSAT Test Prep in Denver, GMAT Test Prep in New York City, ACT Test Prep in Chicago, LSAT Test Prep in Philadelphia, MCAT Test Prep in Miami, SAT Test Prep in Washington DC, SAT Test Prep in Boston, MCAT Test Prep in Washington DC, GMAT Test Prep in Miami

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 #2 : Calculating The Length Of A Radius

Example Question #3 : Calculating The Length Of A Radius

Example Question #4 : Calculating The Length Of A Radius

Example Question #31 : Radius

Example Question #1 : Calculating The Length Of A Radius

Example Question #7 : Calculating The Length Of A Radius

Example Question #2 : Calculating The Length Of A Radius

Example Question #9 : Calculating The Length Of A Radius

Example Question #11 : Calculating The Length Of A Radius

Example Question #301 : Problem Solving Questions

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details