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 #282 : Problem Solving Questions

What is the area of a circle with a diameter of 18cm ?

Possible Answers:

$90\pi cm^2$

$81\pi cm^2$

$324\pi cm^2$

$54\pi cm^2$

$36\pi cm^2$

Correct answer:

$81\pi cm^2$

Explanation:

The area of a circle is defined by $A=\pi r^{2}$ , where is the radius of the circle. We are provided with the diameter of the circle, which is twice the length of .

If d=18cm , then $r=\frac{d}{2}=\frac{18cm}{2}=9cm$

Then, solving for :

$A=\pi r^{2}$

$A=\pi (9cm)^{2}$

$A=81\pi cm^2$

Report an Error

Example Question #51 : Circles

A circle on the coordinate plane is defined by the equation $x^{2}+y^{2}=25$ . What is the area of the circle?

Possible Answers:

$25\pi$

$5\pi$

$50\pi$

$60\pi$

Not enough information provided.

Correct answer:

$25\pi$

Explanation:

The equation of a circle centered at the origin of the coordinate plane is $x^{2}+y^{2}=r^{2}$ , where is the radius of the circle.

The area of the circle, in turn, is defined by the equation $A=\pi r^{2}$ .

Since we are provided with the equation $x^{2}+y^{2}=25$ , we can deduce that $r^{2}=25$ and that $A=25\pi$ .

Report an Error

Example Question #21 : Calculating The Area Of A Circle

What is the area of a circle with a diameter of 20cm ?

Possible Answers:

$100\pi cm^2$

Not enough information provided.

$20\pi cm^2$

$400\pi cm^2$

$40\pi cm^2$

Correct answer:

$100\pi cm^2$

Explanation:

The area of a circle is defined by $A=\pi r^{2}$ , where is the radius of the circle. We are provided with the diameter of the circle, which is twice the length of .

If d=20cm , then $r=\frac{d}{2}=\frac{20cm}{2}=10cm$

Therefore:

$A=\pi r^{2}$

$A=\pi (10cm)^{2}$

$A=100\pi cm^2$

Report an Error

Example Question #51 : Geometry

4c 43438 lg A square is inscribed in a circle of r=5 .

What is the area of the region inside the circle but not inside the square?

Possible Answers:

$25\pi - 50$

$25\pi - 25$

$25\pi$

$\textup{Cannot be determined}$

Correct answer:

$25\pi - 50$

Explanation:

Our first step will be to draw two radii, from the circle's center to two adjacent vertexes of the square, forming a triangle, the third side of which is the edge of the square. Because these radii bisect the square's right angles, we can determine that the triangle we drew is a 45˚ - 45˚ - 90˚ right triangle. Because of the rules governing those isoceles right triangles, we can then determine that, because the two legs of the triangle are 5 (radius = 5), the hypotenuse (the square's side) must equal $5\sqrt{2}$ .

Now we can find the square's area:

$A_{s} = (5\sqrt{2})^{2} = 50$

and the circle's area:

$A_{c} = \pi(5)^{2} = 25\pi$

Finally we subtract the square's area from the circle's area:

$A_{c} - A_{s} = 25\pi - 50$

Report an Error

Example Question #291 : Problem Solving Questions

An engineer is designing a circular hatch for a submarine. If the hatch must have a circumference of 4.56m , what will its area be?

Possible Answers:

.73m^2

1.65m^2

3.14m^2

3.45m^2

Correct answer:

1.65m^2

Explanation:

An engineer is designing a circular hatch for a submarine. If the hatch must have a circumference of 4.56m , what will its area be?

To find area, we will need the radius. We can find the radius using the following formula:

$Circumference=2 \pi r$

So, plug in and solve for r

$4.56m=2 \pi r$

$r\approx.73m$

Next, use the area formula to find the area:

$A_{circle}=\pi r^2$

$A_{circle}=\pi (.73m)^2\approx 1.65m^2$

So we have our answer!

1.65m^2

Report an Error

Example Question #27 : Calculating The Area Of A Circle

and are the area and the diameter of the same circle.

$A = \frac{1}{L}$

$d = t^{2}$ .

Which of the following is a true statement?

Possible Answers:

varies directly as the square of .

varies directly as the fourth power of .

varies directly as the square root of .

varies inversely as the fourth power of .

varies inversely as the square of .

Correct answer:

varies inversely as the fourth power of .

Explanation:

The area and the diameter of a circle are related by the formula

$A = \frac{1}{4} \pi d^{2}$

Substituting:

$\frac{1}{L} = \frac{1}{4} \pi (t^{2}) ^{2}$

$\frac{1}{L} = \frac{\pi t^{4} }{4}$

$L= \frac{4}{\pi t^{4} }$

If $K = \frac{4}{\pi}$ , then

$L = \frac{K}{t^{4}}$ ,

and varies inversely as the fourth power of .

Report an Error

Example Question #21 : Calculating The Area Of A Circle

A circle has radius $\pi ^{t}$ . Give its area.

Possible Answers:

$\pi ^{t+1}$

$\pi ^{t+2}$

$2 \pi ^{2t}$

$2 \pi ^{t+1}$

$\pi ^{2t+1}$

Correct answer:

$\pi ^{2t+1}$

Explanation:

The area of a circle is found using the following formula:

$A = \pi r^{2}$

Set $r= \pi ^{t}$ :

$A = \pi \cdot ( \pi ^{t}) ^{2}$

$A = \pi^{1} \cdot \pi ^{2t}$

$A = \pi ^{2t+1}$

Report an Error

Example Question #26 : Calculating The Area Of A Circle

If the pitcher plant Sarracenia purpurea has a circular opening with a circumference of 6 inches, what is the area of the opening?

Possible Answers:

$A\approx0.95 in^2$

$A\approx 2.86 in^2$

$A\approx 37.70 in^2$

$A\approx 11.45 in^2$

Correct answer:

$A\approx 2.86 in^2$

Explanation:

If the pitcher plant Sarracenia purpurea has a circular opening with a circumference of 6 inches, what is the area of the opening?

We need to work backward from circumference to find area.

Circumference can be found as follows:

$Circ=\pi 2 r$

Use this to find "r" which we will use to find the area:

$6=2 \pi r$

$r=\frac{3}{\pi}$

Next, find area using the following:

$A=\pi r^2$

$A=\pi (\frac{3}{\pi})^2$

$A\approx 2.86 in^2$

Report an Error

Example Question #1 : Calculating The Length Of A Radius

A square and a circle have the same area. What is the ratio of the length of one side of the square to the radius of the circle?

Possible Answers:

$2 \textrm{ to }\sqrt{\pi }$

$\sqrt{\pi } \textrm{ to }1$

$\pi \textrm{ to }1$

$1 \textrm{ to }\pi$

$1 \textrm{ to }\sqrt{\pi }$

Correct answer:

$\sqrt{\pi } \textrm{ to }1$

Explanation:

Let be the sidelength of the square is the square and be the radius of the circle. Then since the areas of the circle and the square are equal, we can set up this equation:

$s^{2 }= \pi r^{2}$

We find the ratio of to - that is, $\frac{s}{r}$ - as follows:

$s^{2 }\div r^{2}= \pi r^{2} \div r^{2}$

$\frac{s^{2 } }{r^{2}} = \pi$

$\sqrt{\frac{s^{2 } }{r^{2}}} =\sqrt{ \pi}$

$\frac{s}{r} =\sqrt{\pi } = \frac{\sqrt{\pi }}{1}$

The correct ratio is $\sqrt{\pi } \textrm{ to }1$ .

Report an Error

Example Question #1 : Calculating The Length Of A Radius

The radius of Circle A is three times the radius of Circle B, which is, in turn, equal to the diameter of Circle C. The sum of their circumferences is $99\pi$ . What is the radius of Circle C?

Possible Answers:

$4 \frac{1}{2}$

$5 \frac{1}{2}$

Correct answer:

$5 \frac{1}{2}$

Explanation:

Let be the radius of circle C. Then Circle B has radius equal to twice this, or , and Circle A has radius equal to three times that, or 3 (2r) = 6r . The circumference of a circle is equal to $2 \pi$ times the radius, so the circumferences of the three circles are:

A: $2 \pi \cdot 6r = 12 \pi r$

B: $2 \pi \cdot 2r = 4 \pi r$

C: $2 \pi r$

These circumferences add up to $99\pi$ , so set up and solve the equation:

$12 \pi r + 4\pi r + 2 \pi r =99 \pi$

$18 \pi r =99 \pi$

$18 \pi r \div 18 \pi =99 \pi \div 18 \pi$

$r =5 \frac{1}{2}$

Report an Error

All GMAT Math Resources

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

Popular Subjects

GRE Tutors in Miami, Chemistry Tutors in Chicago, GMAT Tutors in Phoenix, Computer Science Tutors in Seattle, MCAT Tutors in Denver, ISEE Tutors in San Diego, GMAT Tutors in Denver, Computer Science Tutors in Miami, Chemistry Tutors in New York City, Calculus Tutors in Philadelphia

Popular Courses & Classes

GRE Courses & Classes in Miami, ACT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Philadelphia, LSAT Courses & Classes in Chicago, GMAT Courses & Classes in Washington DC, GMAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Atlanta, ACT Courses & Classes in Phoenix, LSAT Courses & Classes in Seattle, ACT Courses & Classes in Boston

Popular Test Prep

SAT Test Prep in Washington DC, GRE Test Prep in Atlanta, ACT Test Prep in Philadelphia, ACT Test Prep in Boston, MCAT Test Prep in Atlanta, GMAT Test Prep in Seattle, GMAT Test Prep in San Diego, GRE Test Prep in New York City, GMAT Test Prep in Dallas Fort Worth, SAT Test Prep in Denver

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 #282 : Problem Solving Questions

Example Question #51 : Circles

Example Question #21 : Calculating The Area Of A Circle

Example Question #51 : Geometry

Example Question #291 : Problem Solving Questions

Example Question #27 : Calculating The Area Of A Circle

Example Question #21 : Calculating The Area Of A Circle

Example Question #26 : Calculating The Area Of A Circle

Example Question #1 : Calculating The Length Of A Radius

Example Question #1 : Calculating The Length Of A Radius

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details