GRE Math : How to find the percentage of a sector from an angle

Study concepts, example questions & explanations for GRE Math

Create An Account

All GRE Math Resources

13 Diagnostic Tests 452 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1221 : Gre Quantitative Reasoning

A circle of radius $\displaystyle 5$, for an angle $\displaystyle x$, has an arc length of $3\pi$ $\displaystyle 3\pi$. What is the angle $\displaystyle x$?

Gre circle 2

Possible Answers:

$108^{\circ}$ $\displaystyle 108^{\circ}$

$144^{\circ}$ $\displaystyle 144^{\circ}$

$54^{\circ}$ $\displaystyle 54^{\circ}$

$43.2^{\circ}$ $\displaystyle 43.2^{\circ}$

$216^{\circ}$ $\displaystyle 216^{\circ}$

Correct answer:

$108^{\circ}$ $\displaystyle 108^{\circ}$

Explanation:

The formula for an arc length, $\displaystyle l$, of a circle of a given radius, $\displaystyle r$, and a given angle, $\displaystyle x$ is:

$l=2\pi r(\frac{x}{360})$ $\displaystyle l=2\pi r(\frac{x}{360})$

Note that $2\pi r$ $\displaystyle 2\pi r$ is the circumference of the circle.

Conversely, for a known arc length and unknown angle, this equation can be rewritten as follows:

$x=360(\frac{l}{2\pi r})$ $\displaystyle x=360(\frac{l}{2\pi r})$

Plugging in the given values, it is therefore possible to find the missing angle:

$x=360(\frac{3\pi }{2\pi(5 )})=108^{\circ}$ $\displaystyle x=360(\frac{3\pi }{2\pi(5 )})=108^{\circ}$

Report an Error

Example Question #31 : Geometry

Find the radius of the given circle:

Gre circle 3

Possible Answers:

The answer cannot be determined from the information given.

$\displaystyle 9$

$\displaystyle 18$

$\displaystyle 36$

$36\pi$ $\displaystyle 36\pi$

Correct answer:

$\displaystyle 18$

Explanation:

To solve this problem, realize that an inscribed angle (an angle formed by two chords) is equal to twice the central angle formed by connecting the origin to the inscribed angle's endpoints:

Gre circle 3 solution

Now, the formula for an arc length, $\displaystyle l$, of a circle of a given radius, $\displaystyle r$, and a given angle, $\displaystyle x$ is:

$l=2\pi r(\frac{x}{360})$ $\displaystyle l=2\pi r(\frac{x}{360})$

Since the radius is the unknown, this equation can be rewritten as:

$r=(\frac{360}{x})(\frac{l}{2\pi })$ $\displaystyle r=(\frac{360}{x})(\frac{l}{2\pi })$

Plugging in our values, we find:

$r=\frac{360}{60}\frac{6\pi}{2\pi}=18$ $\displaystyle r=\frac{360}{60}\frac{6\pi}{2\pi}=18$

Report an Error

Example Question #32 : Plane Geometry

A given pizza with a $\displaystyle 10$-inch diameter has 1450 $\displaystyle 1450$ calories. A baker cuts the pizza using a $25^{\circ}$ $\displaystyle 25^{\circ}$ angle for each piece. If Susan eats five such pieces, how many calories does she consume? Round to the nearest calorie.

Possible Answers:

503 $\displaystyle 503$

$\displaystyle 75$

375 $\displaystyle 375$

125 $\displaystyle 125$

487 $\displaystyle 487$

Correct answer:

503 $\displaystyle 503$

Explanation:

To solve this, notice that one piece of pizza comprises $\frac{25}{360}$ $\displaystyle \frac{25}{360}$ of the total pie or (reducing) $\frac{5}{72}$ $\displaystyle \frac{5}{72}$ of a pie. Now, if Susan buys five slices, she gets:

$\frac{5}{72} \cdot 5 = \frac{25}{72}$ $\displaystyle \frac{5}{72} \cdot 5 = \frac{25}{72}$ of the pie. If the complete pie contains 1450 $\displaystyle 1450$ calories, she will then eat the following amount of calories:

$\frac{25}{72} \cdot 1450 = 503.47$ $\displaystyle \frac{25}{72} \cdot 1450 = 503.47$

Rounding, this is 503 $\displaystyle 503$ calories.

Report an Error

All GRE Math Resources

13 Diagnostic Tests 452 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Statistics Tutors in Los Angeles, English Tutors in Dallas Fort Worth, GMAT Tutors in Chicago, GMAT Tutors in Miami, Biology Tutors in Dallas Fort Worth, Algebra Tutors in New York City, French Tutors in San Francisco-Bay Area, ISEE Tutors in San Francisco-Bay Area, Computer Science Tutors in San Francisco-Bay Area, LSAT Tutors in Washington DC

Popular Courses & Classes

ACT Courses & Classes in Boston, SSAT Courses & Classes in Chicago, MCAT Courses & Classes in Washington DC, LSAT Courses & Classes in Washington DC, ACT Courses & Classes in Chicago, MCAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Atlanta, Spanish Courses & Classes in Miami, ISEE Courses & Classes in San Diego, LSAT Courses & Classes in Boston

Popular Test Prep

ACT Test Prep in Miami, SSAT Test Prep in Philadelphia, ISEE Test Prep in Seattle, GMAT Test Prep in Miami, GMAT Test Prep in Seattle, LSAT Test Prep in Houston, ISEE Test Prep in Atlanta, LSAT Test Prep in Dallas Fort Worth, GMAT Test Prep in Houston, ACT 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:

GRE Math : How to find the percentage of a sector from an angle

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1221 : Gre Quantitative Reasoning

Example Question #31 : Geometry

Example Question #32 : Plane Geometry

All GRE Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details