We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Basic Geometry : Circles

Study concepts, example questions & explanations for Basic Geometry

Create An Account

All Basic Geometry Resources

9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #101 : Radius

Find the area of a circle that is inscribed in a square that has a diagonal of .

Possible Answers:

$48\pi$

$24\pi$

$40\pi$

$32\pi$

Correct answer:

$32\pi$

Explanation:

When you draw out the circle that is inscribed in a square, you should notice two things. The first thing you should notice is that the diagonal of the square is also the hypotenuse of a right isosceles triangle that has the side lengths of the square as its legs. The second thing you should notice is that the diameter of the circle has the same length as the length of one side of the square.

First, use the Pythagorean theorem to find the length of a side of the square.

$\text{Diagonal}^2=\text{side}^2+\text{side}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Substitute in the length of the diagonal to find the length of the square.

$\text{side}=\frac{16(\sqrt2)}{2}$

Simplify.

$\text{side}=8\sqrt2$

Now, recall the relationship between the diameter of the circle and the side of the square.

$\text{diameter}=\text{side}=8\sqrt2$

Now, recall that the radius is half the length of the diameter.

$\text{radius}=\frac{1}{2}(\text{diameter})$

Substitute in the value o fthe diameter to find the length of the radius.

$\text{radius}=\frac{1}{2}(8\sqrt2)$

Solve.

$\text{radius}=4\sqrt2$

Now, recall the formula to find the area of a circle.

$\text{Area}=\pi\times\text{radius}^2$

Substitute in the value of the radius to find the area of the circle.

$\text{Area}=\pi\times (4\sqrt2)^2$

Solve.

$\text{Area}=32\pi$

Report an Error

Example Question #102 : How To Find The Area Of A Circle

Find the area of a circle that is inscribed in a square that has a diagonal of .

Possible Answers:

$50\pi$

$100\pi$

$75\pi$

$25\pi$

Correct answer:

$50\pi$

Explanation:

First, use the Pythagorean theorem to find the length of a side of the square.

$\text{Diagonal}^2=\text{side}^2+\text{side}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Substitute in the length of the diagonal to find the length of the square.

$\text{side}=\frac{20(\sqrt2)}{2}$

Simplify.

$\text{side}=10\sqrt2$

Now, recall the relationship between the diameter of the circle and the side of the square.

$\text{diameter}=\text{side}=10\sqrt2$

Now, recall that the radius is half the length of the diameter.

$\text{radius}=\frac{1}{2}(\text{diameter})$

Substitute in the value o fthe diameter to find the length of the radius.

$\text{radius}=\frac{1}{2}(10\sqrt2)$

Solve.

$\text{radius}=5\sqrt2$

Now, recall the formula to find the area of a circle.

$\text{Area}=\pi\times\text{radius}^2$

Substitute in the value of the radius to find the area of the circle.

$\text{Area}=\pi\times (5\sqrt2)^2$

Solve.

$\text{Area}=50\pi$

Report an Error

Example Question #103 : How To Find The Area Of A Circle

Find the area of a circle that is inscribed in a square that has a diagonal of .

Possible Answers:

$144\pi$

$12\pi$

$484\pi$

$72\pi$

Correct answer:

$72\pi$

Explanation:

First, use the Pythagorean theorem to find the length of a side of the square.

$\text{Diagonal}^2=\text{side}^2+\text{side}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Substitute in the length of the diagonal to find the length of the square.

$\text{side}=\frac{24(\sqrt2)}{2}$

Simplify.

$\text{side}=12\sqrt2$

Now, recall the relationship between the diameter of the circle and the side of the square.

$\text{diameter}=\text{side}=12\sqrt2$

Now, recall that the radius is half the length of the diameter.

$\text{radius}=\frac{1}{2}(\text{diameter})$

Substitute in the value o fthe diameter to find the length of the radius.

$\text{radius}=\frac{1}{2}(12\sqrt2)$

Solve.

$\text{radius}=6\sqrt2$

Now, recall the formula to find the area of a circle.

$\text{Area}=\pi\times\text{radius}^2$

Substitute in the value of the radius to find the area of the circle.

$\text{Area}=\pi\times (6\sqrt2)^2$

Solve.

$\text{Area}=72\pi$

Report an Error

Example Question #101 : Circles

Find the area of a circle given radius 4.

Possible Answers:

$16\pi$

$64\pi$

$8\pi$

$32\pi$

Correct answer:

$16\pi$

Explanation:

To solve, simply use the formula for the area of a circle. Thus,

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

Report an Error

Example Question #105 : How To Find The Area Of A Circle

If a rectangle with a diagonal of is inscribed in a circle, what is the area of the circle?

Possible Answers:

$4\pi$

Cannot be determined.

$2\pi$

$\pi$

Correct answer:

$\pi$

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

$\text{Diameter}=\text{Diagonal}=2$

Now, recall the relationship between the diameter of a circle and its radius:

$\text{radius}=\frac{1}{2}(\text{Diameter})$

Substitute in the given diameter to find the radius of the circle.

$\text{radius}=\frac{1}{2}(2)$

Simplify.

$\text{radius}=1$

Finally, recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$

Substitute in the value of the radius to find the area.

$\text{Area}=\pi\times(1)^2$

Solve.

$\text{Area}=\pi$

Report an Error

Example Question #106 : How To Find The Area Of A Circle

If a rectangle with a diagonal of is inscribed in a circle, what is the area of the circle?

Possible Answers:

$20\pi$

$8\pi$

$4\pi$

$16\pi$

Correct answer:

$4\pi$

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

$\text{Diameter}=\text{Diagonal}=4$

Now, recall the relationship between the diameter of a circle and its radius:

$\text{radius}=\frac{1}{2}(\text{Diameter})$

Substitute in the given diameter to find the radius of the circle.

$\text{radius}=\frac{1}{2}(4)$

Simplify.

$\text{radius}=2$

Finally, recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$

Substitute in the value of the radius to find the area.

$\text{Area}=\pi\times(2)^2$

Solve.

$\text{Area}=4\pi$

Report an Error

Example Question #101 : Plane Geometry

If a rectangle with a diagonal of $2\sqrt2$ is inscribed in a circle, what is the area of the circle?

Possible Answers:

$2\sqrt2\pi$

$2\pi$

$4\sqrt2\pi$

$16\pi$

Correct answer:

$2\pi$

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

$\text{Diameter}=\text{Diagonal}=2\sqrt2$

Now, recall the relationship between the diameter of a circle and its radius:

$\text{radius}=\frac{1}{2}(\text{Diameter})$

Substitute in the given diameter to find the radius of the circle.

$\text{radius}=\frac{1}{2}(2\sqrt2)$

Simplify.

$\text{radius}=\sqrt2$

Finally, recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$

Substitute in the value of the radius to find the area.

$\text{Area}=\pi\times(\sqrt2)^2$

Solve.

$\text{Area}=2\pi$

Report an Error

Example Question #108 : How To Find The Area Of A Circle

If a rectangle with a diagonal of $4\sqrt2$ is inscribed in a circle, what is the area of the circle?

Possible Answers:

$6\pi$

$12\pi$

$10\pi$

$8\pi$

Correct answer:

$8\pi$

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

$\text{Diameter}=\text{Diagonal}=4\sqrt2$

Now, recall the relationship between the diameter of a circle and its radius:

$\text{radius}=\frac{1}{2}(\text{Diameter})$

Substitute in the given diameter to find the radius of the circle.

$\text{radius}=\frac{1}{2}(4\sqrt2)$

Simplify.

$\text{radius}=2\sqrt2$

Finally, recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$

Substitute in the value of the radius to find the area.

$\text{Area}=\pi\times(2\sqrt2)^2$

Solve.

$\text{Area}=8\pi$

Report an Error

Example Question #102 : Circles

If a rectangle with a diagonal of is inscribed in a circle, what is the area of the circle?

Possible Answers:

$12\pi$

$36\pi$

$24\pi$

Correct answer:

$36\pi$

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

$\text{Diameter}=\text{Diagonal}=12$

Now, recall the relationship between the diameter of a circle and its radius:

$\text{radius}=\frac{1}{2}(\text{Diameter})$

Substitute in the given diameter to find the radius of the circle.

$\text{radius}=\frac{1}{2}(12)$

Simplify.

$\text{radius}=6$

Finally, recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$

Substitute in the value of the radius to find the area.

$\text{Area}=\pi\times(6)^2$

Solve.

$\text{Area}=36\pi$

Report an Error

Example Question #102 : Basic Geometry

If a rectangle with a diagonal of is inscribed in a circle, what is the area of the circle?

Possible Answers:

$72\pi$

$196\pi$

$64\pi$

$80\pi$

Correct answer:

$64\pi$

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

$\text{Diameter}=\text{Diagonal}=16$

Now, recall the relationship between the diameter of a circle and its radius:

$\text{radius}=\frac{1}{2}(\text{Diameter})$

Substitute in the given diameter to find the radius of the circle.

$\text{radius}=\frac{1}{2}(16)$

Simplify.

$\text{radius}=8$

Finally, recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$

Substitute in the value of the radius to find the area.

$\text{Area}=\pi\times(8)^2$

Solve.

$\text{Area}=64\pi$

Report an Error

View Tutors

Jonathan
Certified Tutor

University of Maryland-Baltimore County, Bachelor of Science, Mathematics.

View Tutors

Christie
Certified Tutor

Elizabeth City State University, Bachelor of Education, Education. Gardner-Webb University, Masters in Education, Educational...

View Tutors

Fatimah
Certified Tutor

Yarmuke University, Bachelor of Science, Mathematics.

All Basic Geometry Resources

9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

SAT Tutors in New York City, Computer Science Tutors in Denver, GMAT Tutors in Denver, GMAT Tutors in Phoenix, SSAT Tutors in Washington DC, Biology Tutors in Miami, Computer Science Tutors in Los Angeles, French Tutors in Los Angeles, LSAT Tutors in Houston, Spanish Tutors in San Francisco-Bay Area

Popular Courses & Classes

GMAT Courses & Classes in Washington DC, GRE Courses & Classes in Boston, LSAT Courses & Classes in Miami, Spanish Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in San Diego, GRE Courses & Classes in Miami, LSAT Courses & Classes in Chicago, SSAT Courses & Classes in Miami, ACT Courses & Classes in San Diego

Popular Test Prep

LSAT Test Prep in Miami, ISEE Test Prep in Seattle, SAT Test Prep in Miami, SAT Test Prep in Chicago, LSAT Test Prep in New York City, SAT Test Prep in New York City, LSAT Test Prep in Denver, ACT Test Prep in Houston, LSAT Test Prep in Atlanta, ACT Test Prep in Denver

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

Basic Geometry : Circles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #101 : Radius

Example Question #102 : How To Find The Area Of A Circle

Example Question #103 : How To Find The Area Of A Circle

Example Question #101 : Circles

Example Question #105 : How To Find The Area Of A Circle

Example Question #106 : How To Find The Area Of A Circle

Example Question #101 : Plane Geometry

Example Question #108 : How To Find The Area Of A Circle

Example Question #102 : Circles

Example Question #102 : Basic Geometry

All Basic Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: