We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Math : How to find the area of a circle

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 : Area Of A Circle

What is the area of a circle that has a diameter of inches?

Possible Answers:

960

153.938

706.8583

153.938

176.7146

960

940

Correct answer:

176.7146

Explanation:

The formula for finding the area of a circle is $\pi r^{2}$ . In this formula, represents the radius of the circle. Since the question only gives us the measurement of the diameter of the circle, we must calculate the radius. In order to do this, we divide the diameter by .

$\frac{15}{2}=7.5$

Now we use 7.5 for in our equation.

$\pi (7.5)^{2}=176.7146 \: in^{2}$

Report an Error

Example Question #1 : Area Of A Circle

What is the area of a circle with a diameter equal to 6?

Possible Answers:

$3\pi$

$9\pi$

$18\pi$

$36\pi$

Correct answer:

$9\pi$

Explanation:

First, solve for radius:

$r=\frac{d}{2}=\frac{6}{2}=3$

Then, solve for area:

$A=r^2\pi=3^2\pi=9\pi$

Report an Error

Example Question #1 : Area Of A Circle

The diameter of a circle is $4\ cm$ . Give the area of the circle.

Possible Answers:

$12 \ cm^2$

$11.56\ cm^2$

$13\ cm^2$

$13.56\ cm^2$

$12.56\ cm^2$

Correct answer:

$12.56\ cm^2$

Explanation:

The area of a circle can be calculated using the formula:

$Area=\frac{\pi d^2}{4}$ ,

where is the diameter of the circle, and $\pi$ is approximately 3.14 .

$Area=\frac{\pi d^2}{4}=\frac{\pi\times 4^2}{4}=4\pi \Rightarrow Area\approx 4\times 3.14\Rightarrow Area\approx 12.56 \ cm^2$

Report an Error

Example Question #2 : Area Of A Circle

The diameter of a circle is . Give the area of the circle in terms of .

Possible Answers:

11.56 t^2

12.56 t

12.56 t^2

12 t^2

11.56 t

Correct answer:

12.56 t^2

Explanation:

The area of a circle can be calculated using the formula:

$Area=\frac{\pi d^2}{4}$ ,

where is the diameter of the circle and $\pi$ is approximately 3.14 .

$Area=\frac{\pi (4t)^2}{4}=\frac{16\pi t^2}{4}=4\pi t^2 \Rightarrow Area\approx 4\times 3.14\times t^2$

$\Rightarrow Area\approx 12.56t^2$

Report an Error

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

The radius of a circle is $\frac{2}{\sqrt{\pi }}$ . Give the area of the circle.

Possible Answers:

$4\pi$

$2\pi$

$\frac{4}{\pi }$

Correct answer:

Explanation:

The area of a circle can be calculated as $Area=\pi r^2$ , where is the radius of the circle, and $\pi$ is approximately 3.14 .

$Area=\pi r^2=\pi\times (\frac{2}{\sqrt{\pi}})^2=\pi\times \frac{4}{\pi}\Rightarrow Area=4$

Report an Error

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

The perpendicular distance from the chord to the center of a circle is $\sqrt{2}t$ , and the chord length is $2\sqrt{2}t$ . Give the area of the circle in terms of .

Possible Answers:

11.56t^2

12.56t

11.56t

12t

12.56t^2

Correct answer:

12.56t^2

Explanation:

Chord length = $2\sqrt{r^2-d^2}$ , where is the radius of the circle and is the perpendicular distance from the chord to the circle center.

Chord length = $2\sqrt{r^2-d^2}\Rightarrow (2\sqrt{2})t=2\sqrt{r^2-(\sqrt{2}t)^2}$

$\Rightarrow 8t^2=4(r^2-2t^2)\Rightarrow 4r^2=16t^2\Rightarrow r^2=4t^2\Rightarrow r=2t$

$Area=\pi r^2$ , where is the radius of the circle and $\pi$ is approximately 3.14 .

$Area=\pi r^2=3.14\times (2t)^2=12.56t^2$

Report an Error

Example Question #3 : Area Of A Circle

The circumference of a circle is 12.56 inches. Find the area of the circle.

Let $\pi = 3.14$ .

Possible Answers:

$12\ in^2$

$11.56\ in^2$

$12.56\ in^2$

$11\ in^2$

$13.56\ in^2$

Correct answer:

$12.56\ in^2$

Explanation:

First we need to find the radius of the circle. The circumference of a circle is $Circumference =2\pi r$ , where is the radius of the circle.

$12.56=2\times 3.14\times r\Rightarrow r=2\ in$

The area of a circle is $Area=\pi r^2$ where is the radius of the circle.

$Area=\pi r^2=3.14\times 2^2=12.56\ in^2$

Report an Error

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

Target

In the above figure, OA = AB = BC = CD .

What percent of the figure is shaded gray?

Possible Answers:

$62 \frac{1}{2} \%$

$75 \%$

$66 \frac{2}{3} \%$

$50 \%$

Correct answer:

$62 \frac{1}{2} \%$

Explanation:

For the sake of simplicity, we will assume that OA = AB = BC = CD = 1 ; this reasoning is independent of the actual length.

The four concentric circles have radii 1, 2, 3, and 4, respectively, and their areas can be found by substituting each radius for in the formula $A = \pi r^{2}$ :

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

$A _{2}= \pi r^{2} = \pi \cdot 2^{2} =4 \pi$

$A _{3}= \pi r^{2} = \pi \cdot 3^{2} =9 \pi$

$A _{4}= \pi r^{2} = \pi \cdot 4^{2} =16 \pi$

The outer gray ring is the region between the largest and second-largest circles, and has area

$A _{4} - A _{3} = 16 \pi - 9 \pi = 7 \pi$

The inner gray ring is the region between the second-smallest and smallest circles, and has area

$A _{2} - A _{1} = 4 \pi - \pi = 3 \pi$

The total area of the gray regions is

$7 \pi + 3 \pi = 10 \pi$

Since $10 \pi$ out of total area $16 \pi$ is gray, the percent of the figure that is gray is

$\frac{10 \pi}{16 \pi } \times 100 \% = \frac{5}{8} \times 100 \% =62 \frac{1}{2} \%$ .

Report an Error

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

Target

In the above figure, OA = AB = BC = CD .

Give the ratio of the area of the outer ring to that of the inner circle.

Possible Answers:

7 to 1

9 to 1

16 to 1

12 to 1

Correct answer:

7 to 1

Explanation:

For the sake of simplicity, we will assume that OA = AB = BC = CD = 1 ; this reasoning is independent of the actual length.

The four concentric circles have radii 1, 2, 3, and 4, respectively, and their areas can be found by substituting each radius for in the formula $A = \pi r^{2}$ .

The areas of the largest circle and the second-largest circle are, respectively,

$A _{4}= \pi r^{2} = \pi \cdot 4^{2} =16 \pi$

$A _{3}= \pi r^{2} = \pi \cdot 3^{2} =9 \pi$

The difference of their areas, which is the area of the outer ring, is

$A _{4} - A _{3} = 16 \pi - 9 \pi = 7 \pi$ .

The inner circle has area

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

The ratio of these areas is therefore

$\frac{7 \pi}{\pi} = \frac{7}{1}$ , or 7 to 1.

Report an Error

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

Target

The above figure depicts a dartboard, in which OA = AB = BC = CD .

A blindfolded man throws a dart at the target. Disregarding any skill factor and assuming he hits the target, what are the odds against his hitting the white inner circle?

Possible Answers:

8 to 1

7 to 1

15 to 1

16 to 1

Correct answer:

15 to 1

Explanation:

For the sake of simplicity, we will assume that OA = AB = BC = CD = 1 ; this reasoning is independent of the actual length.

The inner and outer circles have radii 1 and 4, respectively, and their areas can be found by substituting each radius for in the formula $A = \pi r^{2}$ :

$A _{1}= \pi r^{2} = \pi \cdot 1 ^{2} = \pi$ - this is the white inner circle.

$A _{4}= \pi r^{2} = \pi \cdot 4^{2} =16 \pi$

The area of the portion of the target outside the white inner circle is $16 \pi - \pi = 15 \pi$ , so the odds against hitting the inner circle are

$\frac{15 \pi}{\pi} = \frac{15}{1}$ - that is, 15 to 1 odds against.

Report an Error

View Tutors

Evgenii
Certified Tutor

View Tutors

Pavan
Certified Tutor

University of Tennessee, Knoxville, Master's/Graduate, Mechanical Engineering. Pennsylvania State University, Master's/Gradua...

View Tutors

Omar
Certified Tutor

Arizona State University, Bachelors, Civil Engineering.

All ISEE Upper Level Math Resources

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

Popular Subjects

LSAT Tutors in Phoenix, Reading Tutors in Boston, GMAT Tutors in Phoenix, GMAT Tutors in Houston, SAT Tutors in Boston, Algebra Tutors in Dallas Fort Worth, Biology Tutors in San Diego, Algebra Tutors in Phoenix, GRE Tutors in Boston, Statistics Tutors in Denver

Popular Courses & Classes

GMAT Courses & Classes in Phoenix, ISEE Courses & Classes in Phoenix, MCAT Courses & Classes in Washington DC, SAT Courses & Classes in Washington DC, Spanish Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Atlanta, MCAT Courses & Classes in Los Angeles, GRE Courses & Classes in Chicago, MCAT Courses & Classes in Miami, ISEE Courses & Classes in Chicago

Popular Test Prep

GRE Test Prep in San Diego, GRE Test Prep in Miami, SAT Test Prep in Washington DC, GMAT Test Prep in Dallas Fort Worth, SSAT Test Prep in Los Angeles, GMAT Test Prep in Seattle, GMAT Test Prep in Phoenix, MCAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Washington DC, ACT 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 Math : How to find the area of a circle

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #1 : Area Of A Circle

Example Question #1 : Area Of A Circle

Example Question #1 : Area Of A Circle

Example Question #2 : Area Of A Circle

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

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

Example Question #3 : Area Of A Circle

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

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

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

All ISEE Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: