Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Math : How to find the length of an arc

Study concepts, example questions & explanations for ISEE Upper Level Math

Create An Account

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Sectors

A giant clock has a minute hand six feet long. How far, in inches, did the tip move between noon and 1:20 PM?

Possible Answers:

$768 \pi \textrm{ in}$

$192 \pi \textrm{ in}$

$384 \pi \textrm{ in}$

$48 \pi \textrm{ in}$

$96\pi \textrm{ in}$

Correct answer:

$192 \pi \textrm{ in}$

Explanation:

The distance that the tip of the minute hand moves during one hour is the circumference of a circle with radius 6 feet. This circumference is $2\pi r = 2 \pi \times 6 = 12\pi$ feet. One hour and twenty minutes is $1 \frac{1}{3}$ hours, so the tip of the hand moved $1 \frac{1}{3} \times 12 \pi = 16 \pi$ feet, or $16 \pi \times 12 = 192 \pi$ inches.

Report an Error

Example Question #2 : Sectors

A giant clock has a minute hand three feet long. How far, in inches, did the tip move between noon and 12:20 PM?

Possible Answers:

$36\pi \textrm{ in}$

$12\pi \textrm{ in}$

$24\pi \textrm{ in}$

$18\pi \textrm{ in}$

It is impossible to tell from the information given

Correct answer:

$24\pi \textrm{ in}$

Explanation:

The distance that the tip of the minute hand moves during one hour is the circumference of a circle with radius feet. This circumference is $2\pi r = 2 \pi \times 3 = 6\pi$ feet. minutes is one-third of an hour, so the tip of the minute hand moves $\frac{1}{3} \times 6\pi = 2\pi$ feet, or $2\pi \times 12 = 24\pi$ inches.

Report an Error

Example Question #3 : How To Find The Length Of An Arc

Inscribed

In the above figure, express in terms of .

Possible Answers:

$y = x- \frac{27}{4}$

$y = x- \frac{1}{4}$

$y = \frac{1}{2}x - \frac{3}{2}$

$y = \frac{1}{2}x - 10$

Correct answer:

$y = x- \frac{27}{4}$

Explanation:

The measure of an arc - $\overarc{AB}$ - intercepted by an inscribed angle - $\angle ACB$ - is twice the measure of that angle, so

$m \overarc{AB} = 2 \cdot m \angle ACB$

4y + 13 = 2 (2x- 7)

4y + 13 = 4x- 14

4y + 13 - 13 = 4x- 14 - 13

4y = 4x- 27

$\frac{4y}{4} = \frac{4x- 27}{4}$

$y = x- \frac{27}{4}$

Report an Error

Example Question #213 : Geometry

Intercepted

In the above diagram, radius OA = 12 .

Give the length of $\overarc {AB}$ .

Possible Answers:

$\frac{48 \pi }{5}$

$\frac{288\pi }{5}$

$\frac{72 \pi }{5}$

$\frac{24 \pi }{5}$

Correct answer:

$\frac{48 \pi }{5}$

Explanation:

The circumference of a circle is $2 \pi$ multiplied by its radius , so

$C = 2 \pi \cdot OA = 2 \pi \cdot 12 = 24 \pi$ .

$\angle ACB$ , being an inscribed angle of the circle, intercepts an arc $\overarc {AB}$ with twice its measure:

$m \overarc {AB} = 2 \cdot m\angle ACB = 2 \cdot 72 ^{\circ } = 144 ^{\circ }$

The length of $\overarc {AB}$ is the circumference multiplied by $\frac{144}{360}$ :

$\frac{144}{360} \times 24 \pi = \frac{48 \pi }{5}$ .

Report an Error

Example Question #2 : How To Find The Length Of An Arc

While visiting a history museum, you see a radar display which consists of a circular screen with a highlighted wedge with an angle of $65^{\circ}$ . If the screen has a radius of 4 inches, what is the length of the arc of the highlighted wedge?

Possible Answers:

1.44in

4.54in

$3.01\pi in$

$4.54\pi in$

Correct answer:

4.54in

Explanation:

To begin, let's recall our formula for length of an arc.

$Arc=\frac{\theta}{360^{\circ}}2 \pi r$

Now, just plug in and simplify

$Arc=\frac{65^{\circ}}{360^{\circ}}2 \pi (4in)=\frac{13^{\circ}}{9^{\circ}}\pi in\approx 4.54in$

So, our answer is 4.54in

Report an Error

View Tutors

Gabby
Certified Tutor

University of Oregon, Bachelor in Arts, Journalism. University of Oregon, Current Grad Student, Communication, General.

View Tutors

Eva
Certified Tutor

Technicka Univerzita Liberec, Bachelor of Education, Education.

View Tutors

Jaleesa
Certified Tutor

Pomona College, Bachelors, Africana Studies.

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ACT Tutors in Houston, LSAT Tutors in Boston, Algebra Tutors in San Francisco-Bay Area, Statistics Tutors in Boston, Reading Tutors in Chicago, English Tutors in Dallas Fort Worth, MCAT Tutors in Seattle, English Tutors in Seattle, Computer Science Tutors in Miami, Physics Tutors in San Francisco-Bay Area

Popular Courses & Classes

MCAT Courses & Classes in Atlanta, SSAT Courses & Classes in Boston, GRE Courses & Classes in San Diego, ACT Courses & Classes in Philadelphia, MCAT Courses & Classes in Seattle, MCAT Courses & Classes in Philadelphia, SAT Courses & Classes in New York City, ACT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Chicago, LSAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

GMAT Test Prep in Atlanta, MCAT Test Prep in Dallas Fort Worth, MCAT Test Prep in Los Angeles, GRE Test Prep in Houston, MCAT Test Prep in Houston, MCAT Test Prep in Philadelphia, ISEE Test Prep in Philadelphia, SAT Test Prep in Denver, ISEE Test Prep in Miami, SSAT Test Prep in San Diego

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

ISEE Upper Level Math : How to find the length of an arc

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #1 : Sectors

Example Question #2 : Sectors

Example Question #3 : How To Find The Length Of An Arc

Example Question #213 : Geometry

Example Question #2 : How To Find The Length Of An Arc

All ISEE Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: