Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : Sectors

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 #61 : Circles

Find the area of a sector if it has an arc length of $3\pi$ and a radius of 5.7 .

Possible Answers:

26.86

23.11

25.99

24.09

Correct answer:

26.86

Explanation:

The length of the arc of the sector is just a fraction of the arc of the circumference. The area of the sector will be the same fraction of the area as the length of the arc is of the circumference.

We can then write the following equation to find the area of the sector:

$\text{Area}=\frac{\text{Arc Length}}{2\pi r}\pi r^2$

The equation can be simplified to the following:

$\text{Area}=\frac{\text{Arc Length}(r)}{2}$

Plug in the given arc length and radius to find the area of the sector.

$\text{Area}=\frac{3\pi(5.7)}{2}=26.86$

Make sure to round to places after the decimal.

Report an Error

Example Question #61 : Intermediate Geometry

Find the area of a sector if it has an arc length of $10\pi$ and a radius of .

Possible Answers:

171.41

192.59

186.21

188.50

Correct answer:

188.50

Explanation:

The length of the arc of the sector is just a fraction of the arc of the circumference. The area of the sector will be the same fraction of the area as the length of the arc is of the circumference.

We can then write the following equation to find the area of the sector:

$\text{Area}=\frac{\text{Arc Length}}{2\pi r}\pi r^2$

The equation can be simplified to the following:

$\text{Area}=\frac{\text{Arc Length}(r)}{2}$

Plug in the given arc length and radius to find the area of the sector.

$\text{Area}=\frac{12\pi(10)}{2}=188.50$

Make sure to round to places after the decimal.

Report an Error

Example Question #32 : How To Find The Area Of A Sector

Find the area of a sector if it has an arc length of $15\pi$ and a radius of 10.4 .

Possible Answers:

245.04

251.59

214.81

199.44

Correct answer:

245.04

Explanation:

The length of the arc of the sector is just a fraction of the arc of the circumference. The area of the sector will be the same fraction of the area as the length of the arc is of the circumference.

We can then write the following equation to find the area of the sector:

$\text{Area}=\frac{\text{Arc Length}}{2\pi r}\pi r^2$

The equation can be simplified to the following:

$\text{Area}=\frac{\text{Arc Length}(r)}{2}$

Plug in the given arc length and radius to find the area of the sector.

$\text{Area}=\frac{15\pi(10.4)}{2}=245.04$

Make sure to round to places after the decimal.

Report an Error

Example Question #31 : How To Find The Area Of A Sector

Find the area of a sector if it has an arc length of $19\pi$ and a radius of .

Possible Answers:

1521.20

1428.58

1492.26

1304.51

Correct answer:

1492.26

Explanation:

The length of the arc of the sector is just a fraction of the arc of the circumference. The area of the sector will be the same fraction of the area as the length of the arc is of the circumference.

We can then write the following equation to find the area of the sector:

$\text{Area}=\frac{\text{Arc Length}}{2\pi r}\pi r^2$

The equation can be simplified to the following:

$\text{Area}=\frac{\text{Arc Length}(r)}{2}$

Plug in the given arc length and radius to find the area of the sector.

$\text{Area}=\frac{19\pi(50)}{2}=1492.26$

Make sure to round to places after the decimal.

Report an Error

Example Question #33 : How To Find The Area Of A Sector

Find the area of a sector if it has an arc length of and a radius of $12\pi$ .

Possible Answers:

77.91

81.08

75.40

90.36

Correct answer:

75.40

Explanation:

The length of the arc of the sector is just a fraction of the arc of the circumference. The area of the sector will be the same fraction of the area as the length of the arc is of the circumference.

We can then write the following equation to find the area of the sector:

$\text{Area}=\frac{\text{Arc Length}}{2\pi r}\pi r^2$

The equation can be simplified to the following:

$\text{Area}=\frac{\text{Arc Length}(r)}{2}$

Plug in the given arc length and radius to find the area of the sector.

$\text{Area}=\frac{4(12\pi)}{2}=75.40$

Make sure to round to places after the decimal.

Report an Error

Example Question #66 : Circles

Find the area of a sector if it has an arc length of and a radius of $20\sqrt3$ .

Possible Answers:

233.90

259.81

241.20

215.29

Correct answer:

259.81

Explanation:

The length of the arc of the sector is just a fraction of the arc of the circumference. The area of the sector will be the same fraction of the area as the length of the arc is of the circumference.

We can then write the following equation to find the area of the sector:

$\text{Area}=\frac{\text{Arc Length}}{2\pi r}\pi r^2$

The equation can be simplified to the following:

$\text{Area}=\frac{\text{Arc Length}(r)}{2}$

Plug in the given arc length and radius to find the area of the sector.

$\text{Area}=\frac{15(20\sqrt3)}{2}=259.81$

Make sure to round to places after the decimal.

Report an Error

Example Question #67 : Circles

Find the area of a sector if it has an arc length of $13\pi$ and a radius of $49\sqrt3$ .

Possible Answers:

1441.20

1733.09

1720.91

1695.48

Correct answer:

1733.09

Explanation:

The length of the arc of the sector is just a fraction of the arc of the circumference. The area of the sector will be the same fraction of the area as the length of the arc is of the circumference.

We can then write the following equation to find the area of the sector:

$\text{Area}=\frac{\text{Arc Length}}{2\pi r}\pi r^2$

The equation can be simplified to the following:

$\text{Area}=\frac{\text{Arc Length}(r)}{2}$

Plug in the given arc length and radius to find the area of the sector.

$\text{Area}=\frac{13\pi(49\sqrt3)}{2}=1733.09$

Make sure to round to places after the decimal.

Report an Error

Example Question #32 : How To Find The Area Of A Sector

Find the area of a sector if it has an arc length of and a radius of $20\sqrt2$ .

Possible Answers:

268.70

255.64

210.40

249.17

Correct answer:

268.70

Explanation:

The length of the arc of the sector is just a fraction of the arc of the circumference. The area of the sector will be the same fraction of the area as the length of the arc is of the circumference.

We can then write the following equation to find the area of the sector:

$\text{Area}=\frac{\text{Arc Length}}{2\pi r}\pi r^2$

The equation can be simplified to the following:

$\text{Area}=\frac{\text{Arc Length}(r)}{2}$

Plug in the given arc length and radius to find the area of the sector.

$\text{Area}=\frac{19(20\sqrt2)}{2}=268.70$

Make sure to round to places after the decimal.

Report an Error

Example Question #33 : How To Find The Area Of A Sector

Find the area of a sector if it has a central angle of 172 degrees and a radius of .

Possible Answers:

384.25

891.41

701.02

722.39

Correct answer:

384.25

Explanation:

The circle in question can be drawn as shown by the figure below:

Since the area of a sector is just a fractional part of the area of a circle, we can write the following equation to find the area of a sector:

$\text{Area of Sector}=\frac{\text{Central angle}}{360}\pi r^2$ , where is the radius of the circle.

Plug in the given central angle and radius to find the area of the sector.

$\text{Area of Sector}=\frac{172}{360}\pi(16)^2=384.25$

Make sure to round to two places after the decimal.

Report an Error

Example Question #41 : How To Find The Area Of A Sector

Give the area of a sector of a circle if its central angle is $20^{\circ }$ and the length of its arc is 10 inches. Write the answer in terms of $\pi$ , if applicable.

Possible Answers:

$\frac{450}{\pi }\;in^{2}$

$\frac{\sqrt{450}}{\pi }\;in^{2}$

$300\pi \; in^{2}$

$\frac{900}{\pi }\;in^{2}$

$450\pi \; in^{2}$

Correct answer:

$\frac{450}{\pi }\;in^{2}$

Explanation:

The arc of the $20^{\circ }$ sector measures 10 inches, so the circumference of the entire circle is

$C=10 \cdot\frac{360}{20}=180$

The radius is therefore

$r=\frac{C}{2\pi }=\frac{180}{2\pi }=\frac{90}{\pi }$

The area of a $20^{\circ }$ sector of this circle measures:

$A = \frac{20}{360}\cdot\pi r^{2}= \frac{20}{360}\cdot\pi \cdot \left (\frac{90}{\pi } \right )^{2}$

$=\frac{20\cdot 90\cdot 90\cdot \pi }{360\cdot \pi \cdot \pi }=\frac{450}{\pi }$

Report an Error

View Tutors

Tracy
Certified Tutor

Clarion University of Pennsylvania, Bachelor of Science, Physics.

View Tutors

Nicole
Certified Tutor

Western Governors University, Bachelor of Education, Special Education.

View Tutors

Sharif
Certified Tutor

NCCU, Bachelors, Physics and Mathematics.

All Intermediate Geometry Resources

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

Popular Subjects

Statistics Tutors in Miami, Chemistry Tutors in Denver, Calculus Tutors in Seattle, Math Tutors in Houston, Reading Tutors in New York City, English Tutors in Miami, ISEE Tutors in Dallas Fort Worth, English Tutors in Los Angeles, Biology Tutors in San Diego, LSAT Tutors in Chicago

Popular Courses & Classes

MCAT Courses & Classes in New York City, MCAT Courses & Classes in San Diego, Spanish Courses & Classes in Boston, GRE Courses & Classes in Atlanta, ISEE Courses & Classes in Miami, GMAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Seattle, Spanish Courses & Classes in New York City, LSAT Courses & Classes in Atlanta, GMAT Courses & Classes in Phoenix

Popular Test Prep

ACT Test Prep in Philadelphia, MCAT Test Prep in Atlanta, LSAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Phoenix, MCAT Test Prep in Chicago, GMAT Test Prep in Miami, GRE Test Prep in Los Angeles, SAT Test Prep in Miami, GRE Test Prep in Atlanta, SAT Test Prep in Seattle

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 : Sectors

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #61 : Circles

Example Question #61 : Intermediate Geometry

Example Question #32 : How To Find The Area Of A Sector

Example Question #31 : How To Find The Area Of A Sector

Example Question #33 : How To Find The Area Of A Sector

Example Question #66 : Circles

Example Question #67 : Circles

Example Question #32 : How To Find The Area Of A Sector

Example Question #33 : How To Find The Area Of A Sector

Example Question #41 : How To Find The Area Of A Sector

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: