Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

Create An Account

All Intermediate Geometry Resources

8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : How To Find The Angle Of A Sector

What is the angle of a sector of area in^2 on a circle having a radius of $15\:in$ ?

Possible Answers:

$72.00^{\circ}$

$15.22^{\circ}$

$22.92^{\circ}$

$0.06^{\circ}$

$3.00^{\circ}$

Correct answer:

$22.92^{\circ}$

Explanation:

To begin, you should compute the complete area of the circle:

$A=\pi r^2$

For your data, this is:

$A=15^2\pi=225\pi$

Now, to find the angle measure of a sector, you find what portion of the circle the sector is. Here, it is:

$\frac{45}{225\pi}$

Now, multiply this by the total 360 degrees in a circle:

$\frac{45}{225\pi}*360=22.918311805212$

Rounded, this is $22.92^{\circ}$ .

Report an Error

Example Question #21 : Circles

What is the angle of a sector that has an arc length of 13.5 on a circle of diameter ?

Possible Answers:

$194.14^{\circ}$

$10.74^{\circ}$

$128.92^{\circ}$

$35.81^{\circ}$

$14.24^{\circ}$

Correct answer:

$128.92^{\circ}$

Explanation:

The first thing to do for this problem is to compute the total circumference of the circle. Notice that you were given the diameter. The proper equation is therefore:

$C=\pi d$

For your data, this means,

$C=12\pi$

Now, to compute the angle, note that you have a percentage of the total circumference, based upon your arc length:

$\frac{13.5}{12\pi}*360=128.9155039044336$

Rounded to the nearest hundredth, this is $128.92^{\circ}$ .

Report an Error

Example Question #1 : How To Find The Angle Of A Sector

What is the sector angle, in degrees, if the area of the sector is $4\pi$ with a given radius of ?

Possible Answers:

$45^{\circ}$

$360^{\circ}$

$0^{\circ}$

$90^{\circ}$

$60^{\circ}$

Correct answer:

$90^{\circ}$

Explanation:

Write the formula for the area of a circular sector.

$A= \frac{\Theta }{360}\pi r^2$

Substitute the given information and solve for theta:

$4\pi= \frac{\Theta }{360}\pi (4)^2$

$\frac{1}{4}= \frac{\Theta }{360}$

$\Theta= \frac{360}{4} = 90^{\circ}$

Report an Error

Example Question #1 : How To Find The Angle Of A Sector

The length of the intercepted arc of a sector of a circle with radius $\small 12$ meters is $\small \small 4\pi$ meters. Find the measure of the central angle of the sector.

Possible Answers:

$\small 135^\circ$

$\small 15^\circ$

$\small 45^\circ$

$\small 30^\circ$

$\small 60^\circ$

Correct answer:

$\small 60^\circ$

Explanation:

The formula for the length of an arc is

$\small s=\frac{m}{360}2\pi r$

where $\small m$ is measure of the central angle and $\small r$ is the radius. Substituting what we know gives.

$\small \small 4\pi=\frac{m}{360}(2\pi)(12)$

$\small \small 4\pi=\frac{m\pi}{15}$

$\small \small 60\pi=m\pi$

$\small \small m=60$

Therefore, our central angle has a measure of $\small 60^\circ$

Report an Error

Example Question #3 : How To Find The Angle Of A Sector

A sector in a circle with a radius of has an area of $12\pi$ . In degrees, what is the measurement of the central angle for this sector?

Possible Answers:

$45^\circ$

$15^\circ$

$60^\circ$

$30^\circ$

Correct answer:

$30^\circ$

Explanation:

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times12\pi}{\pi\times 12^2}=\frac{4320\pi}{144\pi}=30$

The central angle is degrees.

Report an Error

Example Question #103 : Plane Geometry

A sector in a circle with a radius of has an area of $12\pi$ . In degrees, what is the measurement of the central angle of the sector?

Possible Answers:

$255^\circ$

$285^\circ$

$270^\circ$

$240^\circ$

Correct answer:

$270^\circ$

Explanation:

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times12\pi}{\pi\times 4^2}=\frac{4320\pi}{16\pi}=270$

The central angle is 270 degrees.

Report an Error

Example Question #5 : How To Find The Angle Of A Sector

A sector in a circle with a radius of has an area of $\pi$ . In degrees, what is the measurement of the central angle of the sector?

Possible Answers:

$5^\circ$

$10^\circ$

$15^\circ$

$20^\circ$

Correct answer:

$10^\circ$

Explanation:

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times \pi}{\pi\times 6^2}=\frac{360\pi}{36\pi}=10$

The central angle is degrees.

Report an Error

Example Question #1 : How To Find The Angle Of A Sector

A sector in a circle with a radius of has an area of $2\pi$ . In degrees, what is the measurement of the central angle in the sector?

Possible Answers:

$34.8^\circ$

$28.8^\circ$

$32.6^\circ$

$30.2^\circ$

Correct answer:

$28.8^\circ$

Explanation:

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times 2\pi}{\pi\times 5^2}=\frac{720\pi}{25\pi}=28.8$

The central angle is 28.8 degrees.

Report an Error

Example Question #1 : How To Find The Angle Of A Sector

A sector in a circle with a radius of has an area of $60\pi$ . In degrees, what is the measurement of the central angle of the sector?

Possible Answers:

$355.5^\circ$

$305.5^\circ$

$332.5^\circ$

$337.5^\circ$

Correct answer:

$337.5^\circ$

Explanation:

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times 60\pi}{\pi\times 8^2}=\frac{21600\pi}{64\pi}=337.5$

The central angle is 337.5 degrees.

Report an Error

Example Question #101 : Sectors

A sector in a circle with a radius of has an area of $3\pi$ . In degrees, what is the measurement of the central angle of the sector?

Possible Answers:

$10.8^\circ$

$11^\circ$

$11.2^\circ$

$11.4^\circ$

Correct answer:

$10.8^\circ$

Explanation:

Recall how to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Measurement of Central Angle}}{360}\times\pi\times r^2$

Since the question asks for the measurement of the central angle, rearrange the equation like thus:

$\text{Measurement of Central Angle}=\frac{360\times\text{Area of Sector}}{\pi\times r^2}$

Plug in the given information to find the measurement of the central angle.

$\text{Measurement of Central Angle}=\frac{360\times 3\pi}{\pi\times 10^2}=\frac{1080\pi}{100\pi}=10.8$

The central angle is 10.8 degrees.

Report an Error

View Tutors

Linda
Certified Tutor

Southern New Hampshire University, Bachelor in Arts, European History.

View Tutors

Sydni
Certified Tutor

Louisiana Tech University, Bachelor of Science, Finance. Louisiana Tech University, Master of Arts Teaching, Mathematics.

View Tutors

Emily
Certified Tutor

Louisiana State University and Agricultural & Mechanical College, Bachelor in Arts, Elementary School Teaching.

All Intermediate Geometry Resources

8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

English Tutors in Seattle, Statistics Tutors in Atlanta, GRE Tutors in Atlanta, French Tutors in Chicago, Reading Tutors in Denver, Spanish Tutors in Philadelphia, Math Tutors in Miami, ISEE Tutors in Dallas Fort Worth, Statistics Tutors in Dallas Fort Worth, Math Tutors in Los Angeles

Popular Courses & Classes

Spanish Courses & Classes in Houston, GRE Courses & Classes in Philadelphia, ACT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Miami, SSAT Courses & Classes in Seattle, ACT Courses & Classes in Atlanta, GRE Courses & Classes in Denver, ACT Courses & Classes in Denver, SAT Courses & Classes in Seattle

Popular Test Prep

SSAT Test Prep in San Diego, LSAT Test Prep in New York City, SAT Test Prep in Phoenix, SAT Test Prep in Philadelphia, ISEE Test Prep in Philadelphia, ACT Test Prep in Denver, GMAT Test Prep in Washington DC, ISEE Test Prep in Houston, ACT Test Prep in Miami, SSAT Test Prep in Los Angeles

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)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #2 : How To Find The Angle Of A Sector

Example Question #21 : Circles

Example Question #1 : How To Find The Angle Of A Sector

Example Question #1 : How To Find The Angle Of A Sector

Example Question #3 : How To Find The Angle Of A Sector

Example Question #103 : Plane Geometry

Example Question #5 : How To Find The Angle Of A Sector

Example Question #1 : How To Find The Angle Of A Sector

Example Question #1 : How To Find The Angle Of A Sector

Example Question #101 : Sectors

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: