We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Circles

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 6 7 8 9 10 11 12 13 Next →

Example Question #94 : Geometry

Circlesquare

As illustrated above, a square has one side that is the diameter of a circle. If the area of the square is 100 units, what is the area of the circle?

Possible Answers:

$100\pi$ units squared

$25\pi$ units squared

$50\pi$ units squared

$5\pi$ units squared

$10\pi$ units squared

Correct answer:

$25\pi$ units squared

Explanation:

Find the length of one side of the square by using the formula for the area of a square, A = s^2 , where is the length of one side, with the given information.

A = s^2

$\rightarrow 100 = s^2$

$\rightarrow \sqrt{100} = \sqrt{s^2}$

$\rightarrow s = 10$ units

Since the side of the square forms the diameter of the circle, half of the side will be the length of the circle's radius. The radius is thus calculated as

$\frac{10}{2} = 5$ units.

Now use this radius in the equation for the area of a circle, $A = \pi r^2$ :

$A = \pi(5)^2$

$\rightarrow A = 25\pi$ units squared

Report an Error

Example Question #391 : Geometry

A 12x16 rectangle is inscribed in a circle. What is the area of the circle?

Possible Answers:

10π

100π

90π

120π

50π

Correct answer:

100π

Explanation:

Explanation: Visualizing the rectangle inside the circle (corners touching the circumference of the circle and the center of the rectangle is the center of the circle) you will see that the rectangle can be divided into 8 congruent right triangles, with the hypotenuse as the radius of the circle. Calculating the radius you divide each side of the rectangle by two for the sides of each right triangle (giving 6 and 8). The hypotenuse (by pythagorean theorem or just knowing right triangle sets) the hypotenuse is give as 10. Area of a circle is given by πr². 10² is 100, so 100π is the area.

Report an Error

Example Question #41 : Radius

A circle has a radius of 5 inches. What is the area of the circle in square inches?

Possible Answers:

100

78.54

31.4

Correct answer:

78.54

Explanation:

The area of a circle is found by squaring the circle's radius and multiplying the result by $\pi$ .

$5^{2}=25$

$\pi \cdot 25=78.54$

Report an Error

Example Question #73 : Circles

A circle is inscribed in a square whose side is 6 in. What is the difference in area between the square and the circle, rounded to the nearest square inch?

Possible Answers:

$11\ in^{2}$

$8\ in^{2}$

$14\ in^{2}$

$12\ in^{2}$

$4\ in^{2}$

Correct answer:

$8\ in^{2}$

Explanation:

The circle is inscribed in a square when it is drawn within the square so as to touch in as many places as possible. This means that the side of the square is the same as the diameter of the circle.

Let $\pi =3.14$

$A_{square}= s^{2} = (6)^{2} = 36 in^{2}$

$A_{circle}= \pi r^{2}=3.14\cdot3^{2}=3.14\cdot9=28.26 in^{2}$

So the approximate difference is in area $8\ \textup{in}^{2}$

Report an Error

Example Question #42 : How To Find The Area Of A Circle

Find the area of the shaded region:

Circle

Possible Answers:

$156\pi m^2$

$100\pi m^2$

$36\pi m^2$

$256\pi m^2$

$144\pi m^2$

Correct answer:

$156\pi m^2$

Explanation:

The formula for the area of a circle is:

$A=\pi (r^2)$

where is the radius of the circle.

In order to find the area of the shaded region, you must subtract the area of the inside circle from the area of the outside circle.

Therefore, the formula becomes:

$A=\pi (r_{outside})^2-\pi (r_{inside})^2$

Plugging in our values, we get:

$A=\pi (16m)^2-\pi (10m)^2$

$A=256\pi m^{2}-100\pi m^{2}=156\pi m^2$

Report an Error

Example Question #43 : How To Find The Area Of A Circle

Find the area of a circle with a circumference of $16\pi m$ .

Possible Answers:

$48\pi m^2$

$16\pi m^2$

$64\pi m^2$

$32\pi m^2$

$52\pi m^2$

Correct answer:

$64\pi m^2$

Explanation:

The formula for the circumference of a circle is:

$C=2\pi r$ ,

where is the radius of the circle.

To solve for the radius, plug in our existing values:

$16\pi m=2\pi r$

r=8m

The formula for the area of a circle is:

$A=\pi (r)^2$ ,

where is the radius of the circle.

Plugging in our values, we get:

$A=\pi (8m)^2 = 64\pi m^2$

Report an Error

Example Question #44 : How To Find The Area Of A Circle

Find the area of the following circle:

Possible Answers:

$59 \pi\ m^2$

$29 \pi\ m^2$

$49 \pi\ m^2$

$39 \pi\ m^2$

$69 \pi\ m^2$

Correct answer:

$49 \pi\ m^2$

Explanation:

The formula for the area of a circle is

$A = \pi (r)^2$ ,

where is the radius of the circle.

Plugging in our values, we get:

$A = \pi (7\ m)^2$

$A = 49 \pi\ m^2$

Report an Error

Example Question #41 : Radius

Two equal circles are cut out of a rectangular sheet of paper with the dimensions 10 by 20. The circles were made to have the greatest possible diameter. What is the approximate area of the paper after the two circles have been cut out?

Figure_2

Possible Answers:

Correct answer:

Explanation:

The length of 20 represents the diameters of both circles. Each circle has a diameter of 10 and since radius is half of the diameter, each circle has a radius of 5. The area of a circle is A = πr² . The area of one circle is 25π. The area of both circles is 50π. The area of the rectangle is (10)(20) = 200. 200 - 50π gives you the area of the paper after the two circles have been cut out. π is about 3.14, so 200 – 50(3.14) = 43.

Report an Error

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

Screen_shot_2013-03-18_at_10.29.01_pm

Kate has a ring-shaped lawn which has an inner radius of 10 feet and an outer radius 25 feet. What is the area of her lawn?

Possible Answers:

325π ft²

525π ft²

175π ft²

275π ft²

125π ft²

Correct answer:

525π ft²

Explanation:

The area of an annulus is

$\pi (R^{2}-r^{2})$

where is the radius of the larger circle, and is the radius of the smaller circle.

$\pi (25^{2}-10^{2})$

$\pi (625-100)$

$525\pi$

Report an Error

Example Question #31 : Radius

A 6 by 8 rectangle is inscribed in a circle. What is the area of the circle?

Possible Answers:

$20\pi$

$10\pi$

$4\pi$

$25\pi$

Correct answer:

$25\pi$

Explanation:

The image below shows the rectangle inscribed in the circle. Dividing the rectangle into two triangles allows us to find the diameter of the circle, which is equal to the length of the line we drew. Using a²+b²= c² we get 6²+ 8² = c². c² = 100, so c = 10. The area of a circle is $A=\pi r^2$ . Radius is half of the diameter of the circle (which we know is 10), so r = 5.

$A=\pi *5^2=25\pi$

Diagram_1

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 10 11 12 13 Next →

View Tutors

Lucille
Certified Tutor

University of Central Florida, Bachelor of Science, Education. University of Central Florida, Doctor of Education, Curriculum...

View Tutors

Fitsum
Certified Tutor

Rutgers University-New Brunswick, Bachelor of Science, Biological and Physical Sciences.

View Tutors

Zahid
Certified Tutor

kurukshetra university haryana , Master's/Graduate, Civil engineering.

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Biology Tutors in San Francisco-Bay Area, English Tutors in Los Angeles, Algebra Tutors in Philadelphia, Algebra Tutors in San Francisco-Bay Area, Reading Tutors in Philadelphia, SAT Tutors in Chicago, Spanish Tutors in Phoenix, English Tutors in Philadelphia, ISEE Tutors in San Francisco-Bay Area, GMAT Tutors in Los Angeles

Popular Courses & Classes

SAT Courses & Classes in Philadelphia, Spanish Courses & Classes in Miami, MCAT Courses & Classes in Chicago, ACT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Houston, Spanish Courses & Classes in Philadelphia, GMAT Courses & Classes in Los Angeles, GRE Courses & Classes in Miami, ISEE Courses & Classes in Philadelphia, MCAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

ACT Test Prep in New York City, SSAT Test Prep in Houston, GMAT Test Prep in San Diego, LSAT Test Prep in Washington DC, LSAT Test Prep in Phoenix, GMAT Test Prep in Los Angeles, LSAT Test Prep in Denver, ACT Test Prep in Philadelphia, GRE Test Prep in Washington DC, GRE 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

High School Math : Circles

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #94 : Geometry

Example Question #391 : Geometry

Example Question #41 : Radius

Example Question #73 : Circles

Example Question #42 : How To Find The Area Of A Circle

Example Question #43 : How To Find The Area Of A Circle

Example Question #44 : How To Find The Area Of A Circle

Example Question #41 : Radius

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

Example Question #31 : Radius

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: