Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Quantitative : How to find the area of a sector

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

Create An Account

All ISEE Upper Level Quantitative Resources

8 Diagnostic Tests 234 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #31 : Circles

Circle A has twice the radius of Circle B. Which is the greater quantity?

(a) The area of a $90^{\circ }$ sector of Circle A

(b) The area of Circle B

Possible Answers:

(a) is greater.

It is impossible to tell from the information given.

(a) and (b) are equal.

(b) is greater.

Correct answer:

(a) and (b) are equal.

Explanation:

Let be the radius of Circle B. The radius of Circle A is therefore .

A $90^{\circ }$ sector of a circle comprises $\frac{90}{360} = \frac{1}{4}$ of the circle. The $90^{\circ }$ sector of circle A has area $\frac{1}{4} \pi (2r)^{2} = \frac{1}{4} \cdot 4 \pi r^{2} = \pi r^{2}$ , the area of Circle B. The two quantities are equal.

Report an Error

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

Generalsector-12

What is the area, rounded to the nearest hundredth, of the sector shaded in circle O in the diagram above?

Possible Answers:

106.94

151.35

17.39

475.29

31.31

Correct answer:

106.94

Explanation:

To find the area of a sector, you need to find a percentage of the total area of the circle. You do this by dividing the sector angle by the total number of degrees in a full circle (i.e. 360 ˚). Thus, for our circle, which has a sector with an angle of ˚, we have a percentage of:

$\frac{81}{360}$

Now, we will multiply this by the total area of the circle. Recall that we find such an area according to the equation:

$A = \pi * r^2$

For our problem, r=12.3

Therefore, our equation is:

$\frac{81}{360} * \pi * 12.3^2 = \frac{12254.49\pi}{360}$

Using your calculator, you can determine that this is approximately 106.94 .

Report an Error

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

Generalsector-12

What is the area, rounded to the nearest hundredth, of the sector shaded in circle O in the diagram above?

Possible Answers:

34.13

19.42

65.13

261.30

88.55

Correct answer:

88.55

Explanation:

$\frac{122}{360}$

Now, we will multiply this by the total area of the circle. Recall that we find such an area according to the equation:

$A = \pi * r^2$

For our problem, r=9.12

Therefore, our equation is:

$\frac{122}{360} * \pi * 9.12^2 = \frac{10147.2768\pi}{360}$

Using your calculator, you can determine that this is approximately 88.55 .

Report an Error

Example Question #41 : Circles

Icecreamcone 2

Refer to the above figure, Which is the greater quantity?

(a) The area of $\bigtriangleup ABC$

(b) The area of the orange semicircle

Possible Answers:

It is impossible to determine which is greater from the information given

(a) and (b) are equal

(b) is the greater quantity

(a) is the greater quantity

Correct answer:

(a) is the greater quantity

Explanation:

$\bigtriangleup ABC$ has two angles of degree measure 45; the third angle must measure 90 degrees, making $\bigtriangleup ABC$ a right triangle.

For the sake of simplicity, let BC = 1 ; the reasoning is independent of the actual length. The legs of a 45-45-90 triangle are congruent, so AB = 1 . The area of a right triangle is half the product of its legs, so

$A = \frac{1}{2} \cdot 1 \cdot 1 = \frac{1}{2} = 0.5$

Also, if BC = 1 , then the orange semicircle has diameter 1 and radius $\frac{1}{2}$ . Its area can be found by substituting $r = \frac{1}{2}$ in the formula:

$A = \frac{1}{2} \cdot \pi r^{2}$

$= \frac{1}{2} \cdot \pi \left ( \frac{1}{2} \right ) ^{2}$

$= \frac{1}{2} \cdot \pi \cdot \left ( \frac{1}{4 } \right )$

$= \frac{1}{8} \cdot \pi$

$\approx 0. 125 \cdot 3.14$

$\approx 0. 3925$

$\bigtriangleup ABC$ has a greater area than the orange semicircle.

Report an Error

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

Refer to the above figure, Which is the greater quantity?

(a) The area of the orange semicircle

(b) The area of $\bigtriangleup ABC$

Possible Answers:

(a) and (b) are equal

It is impossible to determine which is greater from the information given

(a) is the greater quantity

(b) is the greater quantity

Correct answer:

(b) is the greater quantity

Explanation:

$\bigtriangleup ABC$ has two angles of degree measure 60; its third angle must also have measure 60, making $\bigtriangleup ABC$ an equilateral triangle

For the sake of simplicity, let BC = 1 ; the reasoning is independent of the actual length. The area of equilateral $\bigtriangleup ABC$ can be found by substituting s = 1 in the formula

$A = \frac{s^{2}\sqrt{3}}{4}$

$= \frac{1^{2}\sqrt{3}}{4}$

$= \frac{1 \cdot \sqrt{3}}{4}$

$\approx \frac{1.7}{4}$

$\approx 0.425$

Also, if BC = 1 , then the orange semicircle has diameter 1 and radius $\frac{1}{2}$ . Its area can be found by substituting $r = \frac{1}{2}$ in the formula:

$A = \frac{1}{2} \cdot \pi r^{2}$

$= \frac{1}{2} \cdot \pi \left ( \frac{1}{2} \right ) ^{2}$

$= \frac{1}{2} \cdot \pi \cdot \left ( \frac{1}{4 } \right )$

$= \frac{1}{8} \cdot \pi$

$\approx 0. 125 \cdot 3.14$

$\approx 0. 3925$

$\bigtriangleup ABC$ has a greater area than the orange semicircle.

Report an Error

Example Question #6 : How To Find The Area Of A Sector

Circle 1

The above circle, which is divided into sectors of equal size, has diameter 20. Give the area of the shaded region.

Possible Answers:

$\frac{125 \pi }{8}$

$\frac{125 \pi }{4 }$

$125 \pi$

$\frac{125 \pi }{16 }$

Correct answer:

$\frac{125 \pi }{4 }$

Explanation:

The radius of a circle is half its diameter; the radius of the circle in the diagram is half of 20, or 10.

To find the area of the circle, set r = 10 in the area formula:

$A = \pi r ^{2} = \pi \cdot 10 ^{2} = 100 \pi$

The circle is divided into sixteen sectors of equal size, five of which are shaded; the shaded portion is

$\frac{5}{16} \cdot 100 \pi = \frac{500}{16} \pi = \frac{125 \pi }{4 }$ .

Report an Error

View Tutors

Robert
Certified Tutor

University of North Carolina at Chapel Hill, Bachelor in Arts, English. North Carolina Central University, Master of Arts, En...

View Tutors

Caroline
Certified Tutor

University of Florida, Bachelor of Science, Psychology.

View Tutors

Chase
Certified Tutor

Western Governors University, Bachelor of Science, Mathematics.

All ISEE Upper Level Quantitative Resources

8 Diagnostic Tests 234 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

MCAT Tutors in New York City, SAT Tutors in Denver, Calculus Tutors in Atlanta, Biology Tutors in Seattle, Calculus Tutors in New York City, Computer Science Tutors in Miami, French Tutors in Los Angeles, Spanish Tutors in Dallas Fort Worth, Statistics Tutors in Houston, ISEE Tutors in Miami

Popular Courses & Classes

SSAT Courses & Classes in San Diego, LSAT Courses & Classes in Los Angeles, GRE Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Phoenix, ISEE Courses & Classes in Seattle, Spanish Courses & Classes in Chicago, Spanish Courses & Classes in New York City, MCAT Courses & Classes in San Diego

Popular Test Prep

ACT Test Prep in Phoenix, ACT Test Prep in Chicago, GMAT Test Prep in Atlanta, GRE Test Prep in San Diego, ISEE Test Prep in Chicago, MCAT Test Prep in Seattle, MCAT Test Prep in Denver, ISEE Test Prep in New York City, SSAT Test Prep in New York City, GMAT 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

ISEE Upper Level Quantitative : How to find the area of a sector

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #31 : Circles

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

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

Example Question #41 : Circles

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

Example Question #6 : How To Find The Area Of A Sector

All ISEE Upper Level Quantitative Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: