We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Circles

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #21 : Circles

Find the circumference of the following sector:

Possible Answers:

$3 \pi + 8\ m$

$2 \pi + 8\ m$

$3 \pi + 6\ m$

$3 \pi + 12\ m$

$2 \pi + 12\ m$

Correct answer:

$3 \pi + 12\ m$

Explanation:

The formula for the circumference of a sector is

$C = 2 \pi r (part) + 2r$ ,

where is the radius of the sector and part is the fraction of the sector.

Plugging in our values, we get:

$C = 2 \pi (6m)(\frac{90}{360})+2(6m)$

$C= 3 \pi + 12\ m$

Report an Error

Example Question #1 : How To Find The Length Of An Arc

Circle

In the circle above, the angle A in radians is $\frac{\pi}{4}$

What is the length of arc A?

Possible Answers:

$\frac{\pi r}{4}$

$\frac{\pi r}{8}$

$\frac{\pi r}{16}$

$\pi r$

$\frac{\pi r}{2}$

Correct answer:

$\frac{\pi r}{4}$

Explanation:

Circumference of a Circle = $2\pi r$

Arc Length

$=\frac{Angle A}{2\pi}\ast2\pi r$

$=\frac{\frac{\pi}{4}}{2\pi}\ast2\pi r$

$=\frac{\pi}{(4)2\pi}\ast2\pi r$

$=\frac{1}{8}\ast2\pi r=\frac{\pi r}{4}$

Report an Error

Example Question #171 : High School Math

Solve for .

(Figure not drawn to scale).

Possible Answers:

110^o

70^o

55^o

62^o

Correct answer:

55^o

Explanation:

We can solve for the angle, , by using the below relationship.

$\small Inscribed\ angle=\frac{1}{2}Intercepted\ arc$

In the figure, intercepted arc is given.

$\small x=\frac{1}{2}(110^o)$

$\small x=55^o$

Report an Error

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

A pie has a diameter of 12". A piece is cut out, having a surface area of 4.5π. What is the angle of the cut?

Possible Answers:

4.5°

25°

12.5°

45°

90°

Correct answer:

45°

Explanation:

This is simply a matter of percentages. We first have to figure out what percentage of the surface area is represented by 4.5π. To do that, we must calculate the total surface area. If the diameter is 12, the radius is 6. Don't be tricked by this!

A = π * 6 * 6 = 36π

Now, 4.5π is 4.5π/36π percentage or 0.125 (= 12.5%)

To figure out the angle, we must take that percentage of 360°:

0.125 * 360 = 45°

Report an Error

Example Question #271 : Geometry

Eric is riding a Ferris wheel. The Ferris wheel has 18 compartments, numbered in order clockwise. If compartment 1 is at 0 degrees and Eric enters compartment 13, what angle is he at?

Possible Answers:

180

300

260

280

240

Correct answer:

240

Explanation:

12 compartments further means 240 more degrees. 240 is the answer.

360/12 = 240 degrees

Report an Error

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

Solve for $\small n$ .

Possible Answers:

60^o

45^o

120^o

30^o

Correct answer:

60^o

Explanation:

The measure of an arc of an inscribed angle is twice the size of the inscribed angle.

$2*\angle _{in}=\angle _{arc}$

2n=120^o

$n=\frac{120^o}{2}=60^o$

Report an Error

Example Question #41 : Plane Geometry

Circle2

In the figure above that includes Circle O, the measure of angle BAC is equal to 35 degrees, the measure of angle FBD is equal to 40 degrees, and the measure of arc AD is twice the measure of arc AB. Which of the following is the measure of angle CEF? The figure is not necessarily drawn to scale, and the red numbers are used to mark the angles, not represent angle measures.

Possible Answers:

75^o

80^o

60^o

30^o

110^o

Correct answer:

30^o

Explanation:

The measure of angle CEF is going to be equal to half of the difference between the measures two arcs that it intercepts, namely arcs AD and CD.

$\angle CEF=\frac{1}{2}(AD-CD)$

Thus, we need to find the measure of arcs AD and CD. Let's look at the information given and determine how it can help us figure out the measures of arcs AD and CD.

Angle BAC is an inscribed angle, which means that its meausre is one-half of the measure of the arc that it incercepts, which is arc BC.

$\angle BAC=\frac{1}{2}BC$

$35^o=\frac{1}{2}BC\rightarrow BC=70^o$

Thus, since angle BAC is 35 degrees, the measure of arc BC must be 70 degrees.

We can use a similar strategy to find the measure of arc CD, which is the arc intercepted by the inscribed angle FBD.

$40^o=\frac{1}{2}CD\rightarrow CD=80^o$

Because angle FBD has a measure of 40 degrees, the measure of arc CD must be 80 degrees.

We have the measures of arcs BC and CD. But we still need the measure of arc AD. We can use the last piece of information given, along with our knowledge about the sum of the arcs of a circle, to determine the measure of arc AD.

We are told that the measure of arc AD is twice the measure of arc AB. We also know that the sum of the measures of arcs AD, AB, CD, and BC must be 360 degrees, because there are 360 degrees in a full circle.

AD+AB+CD+BC=360^o

AD+AB+80^o+70^o=360^o

AD+AB=210^o

Because AD = 2AB, we can substitute 2AB for AD.

2AB+AB=210^o

3AB=210^o

AB=70^o

This means the measure of arc AB is 70 degrees, and the measure of arc AD is 2(70) = 140 degrees.

Now, we have all the information we need to find the measure of angle CEF, which is equal to half the difference between the measure of arcs AD and CD.

$\angle CEF=\frac{1}{2}(AD-CD)$

$\angle CEF=\frac{1}{2}(140^o-80^o)=\frac{1}{2}(60^o)$

$\angle CEF=30^o$

Report an Error

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

The length of an arc, , of a circle is $8\pi$ and the radius, , of the circle is . What is the measure in degrees of the central angle, $\theta$ , formed by the arc ?

Possible Answers:

30^o

120^o

90^o

60^o

45^o

Correct answer:

90^o

Explanation:

The circumference of the circle is $2\pi r$ .

$2\pi(16)=32\pi$

The length of the arc S is $8\pi$ .

A ratio can be established:

$\frac{S}{\text{circumference}}=\frac{\theta}{360^o}$

$\frac{8\pi}{32\pi}=\frac{\theta}{360^o}$

Solving for $\theta$ yields 90^o.

Note: This makes sense. Since the arc S was one-fourth the circumference of the circle, the central angle formed by arc S should be one-fourth the total degrees of a circle.

Report an Error

Example Question #21 : Circles

Circle

In the circle above, the length of arc BC is 100 degrees, and the segment AC is a diameter. What is the measure of angle ADB in degrees?

Possible Answers:

100

cannot be determined

Correct answer:

Explanation:

Since we know that segment AC is a diameter, this means that the length of the arc ABC must be 180 degrees. This means that the length of the arc AB must be 80 degrees.

Since angle ADB is an inscribed angle, its measure is equal to half of the measure of the angle of the arc that it intercepts. This means that the measure of the angle is half of 80 degrees, or 40 degrees.

Report an Error

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:

$3.00^{\circ}$

$22.92^{\circ}$

$0.06^{\circ}$

$15.22^{\circ}$

$72.00^{\circ}$

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

View Tutors

Joshua
Certified Tutor

Murray State University, Bachelor in Arts, Spanish. Lipscomb University, Bachelor of Science, Teacher Assistant.

View Tutors

Kaylee
Certified Tutor

Brigham Young University, Bachelor, MFA - Animation.

View Tutors

Lydia
Certified Tutor

The Richard Stockton College of New Jersey, Bachelor of Science, Biochemistry and Molecular Biology.

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Reading Tutors in Atlanta, French Tutors in Washington DC, Spanish Tutors in Denver, MCAT Tutors in Seattle, GRE Tutors in Houston, SAT Tutors in Washington DC, Math Tutors in Chicago, English Tutors in Atlanta, Computer Science Tutors in Miami, Calculus Tutors in Denver

Popular Courses & Classes

ACT Courses & Classes in Los Angeles, SAT Courses & Classes in Houston, ISEE Courses & Classes in Houston, SSAT Courses & Classes in Chicago, GMAT Courses & Classes in New York City, ACT Courses & Classes in Denver, ACT Courses & Classes in Philadelphia, LSAT Courses & Classes in Denver, ISEE Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

LSAT Test Prep in Phoenix, GRE Test Prep in Phoenix, ACT Test Prep in Los Angeles, GMAT Test Prep in New York City, SSAT Test Prep in Houston, SSAT Test Prep in San Diego, LSAT Test Prep in Washington DC, SAT Test Prep in Miami, GRE Test Prep in Houston, GMAT Test Prep in Dallas Fort Worth

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

High School Math : Circles

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #21 : Circles

Example Question #1 : How To Find The Length Of An Arc

Example Question #171 : High School Math

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

Example Question #271 : Geometry

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

Example Question #41 : Plane Geometry

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

Example Question #21 : Circles

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

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: