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 #31 : Intermediate Geometry

Circle

The radius of the circle above is $\displaystyle 4$ and $\angle A=45^{\circ}$ $\displaystyle \angle A=45^{\circ}$ . What is the area of the shaded section of the circle?

Possible Answers:

$8\pi$ $\displaystyle 8\pi$

$16\pi$ $\displaystyle 16\pi$

$4\pi$ $\displaystyle 4\pi$

$\pi$ $\displaystyle \pi$

$2\pi$ $\displaystyle 2\pi$

Correct answer:

$2\pi$ $\displaystyle 2\pi$

Explanation:

Area of Circle = πr² = π4²= 16π

Total degrees in a circle = 360

Therefore 45 degree slice = 45/360 fraction of circle = 1/8

Shaded Area = 1/8 * Total Area = 1/8 * 16π = 2π

Report an Error

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

A circle has a diameter of $\displaystyle 60$ meters. A certain sector of the circle has a central angle of $\small 20^\circ$ $\displaystyle \small 20^\circ$ . Find the area of the sector.

Possible Answers:

$\small 200\pi\,m^2$ $\displaystyle \small 200\pi\,m^2$

$\small 50\pi\,m^2$ $\displaystyle \small 50\pi\,m^2$

$\small 6\pi\,m^2$ $\displaystyle \small 6\pi\,m^2$

$\small 30\pi\,m^2$ $\displaystyle \small 30\pi\,m^2$

$\small 25\pi\,m^2$ $\displaystyle \small 25\pi\,m^2$

Correct answer:

$\small 50\pi\,m^2$ $\displaystyle \small 50\pi\,m^2$

Explanation:

The formula for the area of a sector is.

$\small S=\frac{m}{360}\pi r^2$ $\displaystyle \small S=\frac{m}{360}\pi r^2$ where $\small r$ $\displaystyle \small r$ is the radius and $\small m$ $\displaystyle \small m$ is the measure of the central angle of the sector.

We are given that the diameter of the circle is 60. Therefore its radius is simply half as long, or 30.

Substituting into our equation gives

$\small \small S=\frac{20}{360}\pi(30^2)=\frac{1}{18}\pi(900)=50\pi$ $\displaystyle \small \small S=\frac{20}{360}\pi(30^2)=\frac{1}{18}\pi(900)=50\pi$

Therefore our area is $\small 50\pi\,m^2$ $\displaystyle \small 50\pi\,m^2$

Report an Error

Example Question #32 : Circles

Find the area of a sector with a central angle of 124 $\displaystyle 124$ degrees and a radius of $\displaystyle 12$ .

Possible Answers:

155.82 $\displaystyle 155.82$

148.20 $\displaystyle 148.20$

159.22 $\displaystyle 159.22$

156.29 $\displaystyle 156.29$

Correct answer:

155.82 $\displaystyle 155.82$

Explanation:

The circle in question could be depicted as shown in the figure.

Recall the formula for finding the area of a sector of a circle:

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

Since the central angle and the radius are given in the question, plug them in to find the area of the sector.

$\text{Area of Sector}=\frac{124}{360}\times\pi\times 12^2$ $\displaystyle \text{Area of Sector}=\frac{124}{360}\times\pi\times 12^2$

Solve and round to two decimal places.

$\text{Area of Sector}=155.82$ $\displaystyle \text{Area of Sector}=155.82$

Report an Error

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

Find the area of a sector that has a central angle of 129 $\displaystyle 129$ degrees and a radius of $\displaystyle 13$ .

Possible Answers:

192.12 $\displaystyle 192.12$

182.46 $\displaystyle 182.46$

200.01 $\displaystyle 200.01$

190.25 $\displaystyle 190.25$

Correct answer:

190.25 $\displaystyle 190.25$

Explanation:

The circle in question could be depicted as shown in the figure.

Recall the formula for finding the area of a sector of a circle:

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

Since the central angle and the radius are given in the question, plug them in to find the area of the sector.

$\text{Area of Sector}=\frac{129}{360}\times\pi\times 13^2$ $\displaystyle \text{Area of Sector}=\frac{129}{360}\times\pi\times 13^2$

Solve and round to two decimal places.

$\text{Area of Sector}=190.25$ $\displaystyle \text{Area of Sector}=190.25$

Report an Error

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

Find the area of a sector that has a central angle of 130 $\displaystyle 130$ degrees and a radius of $\displaystyle 19$ .

Possible Answers:

485.12 $\displaystyle 485.12$

399.50 $\displaystyle 399.50$

412.29 $\displaystyle 412.29$

409.54 $\displaystyle 409.54$

Correct answer:

409.54 $\displaystyle 409.54$

Explanation:

The circle in question could be depicted as shown in the figure.

Recall the formula for finding the area of a sector of a circle:

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

Since the central angle and the radius are given in the question, plug them in to find the area of the sector.

$\text{Area of Sector}=\frac{130}{360}\times\pi\times 19^2$ $\displaystyle \text{Area of Sector}=\frac{130}{360}\times\pi\times 19^2$

Solve and round to two decimal places.

$\text{Area of Sector}=409.54$ $\displaystyle \text{Area of Sector}=409.54$

Report an Error

Example Question #31 : Plane Geometry

Find the area of a sector that has a central angle of 135 $\displaystyle 135$ degrees and a radius of $\displaystyle 21$ .

Possible Answers:

519.54 $\displaystyle 519.54$

527.02 $\displaystyle 527.02$

529.30 $\displaystyle 529.30$

609.39 $\displaystyle 609.39$

Correct answer:

519.54 $\displaystyle 519.54$

Explanation:

The circle in question could be depicted as shown in the figure.

Recall the formula for finding the area of a sector of a circle:

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

Since the central angle and the radius are given in the question, plug them in to find the area of the sector.

$\text{Area of Sector}=\frac{135}{360}\times\pi\times 21^2$ $\displaystyle \text{Area of Sector}=\frac{135}{360}\times\pi\times 21^2$

Solve and round to two decimal places.

$\text{Area of Sector}=519.54$ $\displaystyle \text{Area of Sector}=519.54$

Report an Error

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

Find the area of a sector that has a central angle of 115 $\displaystyle 115$ degrees and a radius of $\displaystyle 8$ .

Possible Answers:

60.39 $\displaystyle 60.39$

70.05 $\displaystyle 70.05$

64.23 $\displaystyle 64.23$

69.21 $\displaystyle 69.21$

Correct answer:

64.23 $\displaystyle 64.23$

Explanation:

The circle in question could be depicted as shown in the figure.

Recall the formula for finding the area of a sector of a circle:

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

Since the central angle and the radius are given in the question, plug them in to find the area of the sector.

$\text{Area of Sector}=\frac{115}{360}\times\pi\times 8^2$ $\displaystyle \text{Area of Sector}=\frac{115}{360}\times\pi\times 8^2$

Solve and round to two decimal places.

$\text{Area of Sector}=64.23$ $\displaystyle \text{Area of Sector}=64.23$

Report an Error

Example Question #32 : Plane Geometry

Find the area of a sector that has a central angle of 118 $\displaystyle 118$ degrees and a radius of $\displaystyle 10$ .

Possible Answers:

98.45 $\displaystyle 98.45$

101.59 $\displaystyle 101.59$

99.21 $\displaystyle 99.21$

102.97 $\displaystyle 102.97$

Correct answer:

102.97 $\displaystyle 102.97$

Explanation:

The circle in question could be depicted as shown in the figure.

Recall the formula for finding the area of a sector of a circle:

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

Since the central angle and the radius are given in the question, plug them in to find the area of the sector.

$\text{Area of Sector}=\frac{118}{360}\times\pi\times 10^2$ $\displaystyle \text{Area of Sector}=\frac{118}{360}\times\pi\times 10^2$

Solve and round to two decimal places.

$\text{Area of Sector}=102.97$ $\displaystyle \text{Area of Sector}=102.97$

Report an Error

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

Find the area of a sector that has a central angle of $\displaystyle 34$ degrees and a radius of $\displaystyle 5$ .

Possible Answers:

12.66 $\displaystyle 12.66$

6.10 $\displaystyle 6.10$

16.92 $\displaystyle 16.92$

7.42 $\displaystyle 7.42$

Correct answer:

7.42 $\displaystyle 7.42$

Explanation:

The circle in question could be depicted as shown in the figure.

Recall the formula for finding the area of a sector of a circle:

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

Since the central angle and the radius are given in the question, plug them in to find the area of the sector.

$\text{Area of Sector}=\frac{34}{360}\times\pi\times 5^2$ $\displaystyle \text{Area of Sector}=\frac{34}{360}\times\pi\times 5^2$

Solve and round to two decimal places.

$\text{Area of Sector}=7.42$ $\displaystyle \text{Area of Sector}=7.42$

Report an Error

Example Question #39 : Circles

Find the area of a sector that has a central angle of $\displaystyle 26$ degrees and a radius of $\displaystyle 16$ .

Possible Answers:

49.68 $\displaystyle 49.68$

58.08 $\displaystyle 58.08$

42.10 $\displaystyle 42.10$

54.19 $\displaystyle 54.19$

Correct answer:

58.08 $\displaystyle 58.08$

Explanation:

The circle in question could be depicted as shown in the figure.

Recall the formula for finding the area of a sector of a circle:

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

Since the central angle and the radius are given in the question, plug them in to find the area of the sector.

$\text{Area of Sector}=\frac{26}{360}\times\pi\times 16^2$ $\displaystyle \text{Area of Sector}=\frac{26}{360}\times\pi\times 16^2$

Solve and round to two decimal places.

$\text{Area of Sector}=58.08$ $\displaystyle \text{Area of Sector}=58.08$

Report an Error

View Tutors

Andreas
Certified Tutor

University of Wales, Bachelor in Arts, Political Science and Government. University of Exeter, Master of Arts, Political Scie...

View Tutors

Laurie
Certified Tutor

Monmouth College, Bachelor in Arts, English. National Louis University, Master of Arts Teaching, Special Education.

View Tutors

Heather
Certified Tutor

Alvernia University, Bachelor in Arts, English. Kutztown University of Pennsylvania, Master of Arts, English.

All Intermediate Geometry Resources

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

Popular Subjects

LSAT Tutors in Washington DC, Physics Tutors in San Francisco-Bay Area, Algebra Tutors in Atlanta, SAT Tutors in Seattle, Chemistry Tutors in Houston, GMAT Tutors in Chicago, Computer Science Tutors in Washington DC, MCAT Tutors in New York City, SSAT Tutors in Miami, English Tutors in Seattle

Popular Courses & Classes

LSAT Courses & Classes in Philadelphia, MCAT Courses & Classes in San Diego, GMAT Courses & Classes in Atlanta, SAT Courses & Classes in Philadelphia, GRE Courses & Classes in Washington DC, SAT Courses & Classes in Los Angeles, GRE Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Houston, ISEE Courses & Classes in New York City, SAT Courses & Classes in Atlanta

Popular Test Prep

SAT Test Prep in Atlanta, MCAT Test Prep in Seattle, SAT Test Prep in New York City, ISEE Test Prep in Houston, MCAT Test Prep in Boston, GRE Test Prep in Washington DC, SAT Test Prep in Dallas Fort Worth, MCAT Test Prep in Denver, GRE Test Prep in Houston, ACT 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 : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #31 : Intermediate Geometry

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

Example Question #32 : Circles

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

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

Example Question #31 : Plane Geometry

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

Example Question #32 : Plane Geometry

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

Example Question #39 : Circles

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: