Call Now to Set Up Tutoring:

(888) 888-0446

Common Core: 7th Grade Math : Know and Use the Formulas for the Area and Circumference of a Circle: CCSS.Math.Content.7.G.B.4

Study concepts, example questions & explanations for Common Core: 7th Grade Math

Create An Account

All Common Core: 7th Grade Math Resources

7 Diagnostic Tests 110 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : 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:

$12.56\ in^2$

$11.56\ in^2$

$12\ in^2$

$11\ in^2$

$13.56\ in^2$

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 : Radius

The radius of a circle is 4 cm, what is the area?

Possible Answers:

$58.7\ cm^{2}$

$28.3\ cm^{2}$

$12.6\ cm^{2}$

$78\ cm^{2}$

$50.2\ cm^{2}$

Correct answer:

$50.2\ cm^{2}$

Explanation:

The area of a circle is found by: $Area=r^{2}\pi$ , where r is the radius.

$4^{2} \pi = 50.2$ .

The area of the circle is $50.2\ cm^{2}$ .

Report an Error

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

The radius, , of the circle below is 18 units. What is the area of the circle?

Circle

Possible Answers:

$324\pi$ square units

$18\pi$ square units

324 square units

Cannot be determined

$36\pi$ square units

Correct answer:

$324\pi$ square units

Explanation:

The formula for the area, , of a circle with radius is:

$A=\pi R^{2}$

We can fill in

$A=\pi (18^{2})$

$A=324\pi$

You could do the arithmetic to get an area of about 1,017.876 square units, but it is ok and more precise to leave it as shown.

Report an Error

Example Question #11 : Know And Use The Formulas For The Area And Circumference Of A Circle: Ccss.Math.Content.7.G.B.4

Give the area of a circle with diameter 13.

Possible Answers:

$26 \pi$

$13 \pi$

$\frac{169\pi }{2}$

$\frac{169\pi }{4}$

$\frac{13\pi }{2}$

Correct answer:

$\frac{169\pi }{4}$

Explanation:

Half of the diameter 13 is the radius $\frac{13}{2}$ . Use the area formula:

$A = \pi r^{2} = \pi \cdot \left ( \frac{13}{2} \right )^{2} = \frac{169\pi }{4}$

Report an Error

Example Question #22 : Radius

How many times greater is the area of a circle with a radius of 4in., compared to a circle with a radius of 2in.?

Possible Answers:

$4$

$2\pi$

$\pi$

$2$

$4\pi$

Correct answer:

$4$

Explanation:

The area of a circle can be solved using the equation $A=\pi r^{2}$

The area of a circle with radius 4 is $\pi 4^{2}=16\pi$ while the area of a circle with radius 2 is $\pi 2^{2}=4\pi$ . $16\pi \div 4\pi =4$

Report an Error

Example Question #11 : Area Of A Circle

Find the area of a circle that has a radius of $\frac{1}{5}$ .

Possible Answers:

$\frac{1}{5}$

$\frac{1}{25}\pi$

$\frac{2}{5}\pi$

$\frac{1}{10}\pi$

Correct answer:

$\frac{1}{25}\pi$

Explanation:

Use the following formula to find the area of a circle:

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

For the circle in question, plug in the given radius to find the area.

In our particular case the radius is $\frac{1}{5}$ .

$\text{Area}=\pi \times \left(\frac{1}{5}\right)^2=\frac{1}{25}\pi$

When squarring a fraction we need to square both the numerator and the denominator.

$\pi \times \left(\frac{1}{5}\right)^2=\frac{1^2}{5^2}\pi=\frac{1\cdot 1}{5\cdot 5}\pi=\frac{1}{25}\pi$

Report an Error

Example Question #12 : Area Of A Circle

Find the area of a circle that has a radius of $\sqrt5$ .

Possible Answers:

$2\sqrt5 \pi$

$\sqrt{5}\pi$

$\sqrt{10}\pi$

$5\pi$

Correct answer:

$5\pi$

Explanation:

Use the following formula to find the area of a circle:

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

For the circle in question, plug in the given radius to find the area.

In this problem the known radius is $\sqrt5$

Now plug the radius into the area equation.

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

Therefore we get,

$\text{Area}=\pi \times (\sqrt5)^2=5\pi$

Recall that when a square root is squared you are left with the number under the square root sign. This happens because when you square a number you are multiplying it by itself. In our case this is,

$(\sqrt{5})^2=\sqrt{5}\cdot \sqrt{5}$ .

From here we can use the property of multiplication and radicals to rewrite our expression as follows,

$\sqrt{5}\cdot \sqrt{5}=\sqrt{5\cdot 5}$

and when there are two numbers that are the same under a square root sign you bring out one and the other number and square root sign go away.

$\sqrt{5\cdot 5}=5$

Report an Error

Example Question #11 : Radius

What is the area of a circle with a diameter of , rounded to the nearest whole number?

Possible Answers:

$\dpi{100} 64$

$\dpi{100} 255$

$\dpi{100} 254$

$\dpi{100} 81$

Correct answer:

$\dpi{100} 64$

Explanation:

The formula for the area of a circle is

$\dpi{100} \pi r^{2}$

Find the radius by dividing 9 by 2:

$\dpi{100} \frac{9}{2}=4.5$

So the formula for area would now be:

$\dpi{100} \pi r^{2}=\pi (4.5)^{2}=20.25\pi \approx 63.6= 64$

Report an Error

Example Question #141 : How To Find The Area Of A Circle

If this circle has a diameter of 12 inches, what is its area?

Circle_12d

Possible Answers:

$26\pi\ \text{inches}^{2}$

$36\pi\ \text{inches}^{2}$

$48\pi\ \text{inches}^{2}$

$116\ \text{inches}^{2}$

None of the other answers are correct.

Correct answer:

$36\pi\ \text{inches}^{2}$

Explanation:

To find the area, we need to determine the radius of the circle first.

The radius is calculated as $r=\frac{D}{2}$ , where D is the diameter.

Given that the diameter is 12 inches, the radius is $r=\frac{12}{2}$ , or $r=6\ \text{inches}$ .

Next, we know that the formula for the area of the circle is $A=\pi r^2$ .

Using the radius we just found, we can find the area:

$A=\pi (6)^2=36\pi\ \text{inches}$

Report an Error

Example Question #13 : Area Of A Circle

What is the area of the circle provided?

Possible Answers:

$6\pi\textup{ in}^2$

$9\pi\textup{ in}^2$

$8\pi\textup{ in}^2$

$7\pi\textup{ in}^2$

$5\pi\textup{ in}^2$

Correct answer:

$9\pi\textup{ in}^2$

Explanation:

In order to solve this problem, we need to recall the formula for the area of a circle:

$A= r^2\pi$

The circle in this question provides us with the radius, so we can use the formula to solve:

$A=3^2\pi$

Solve:

$A=9\pi\textup{ in}^2$

Report an Error

View Tutors

David
Certified Tutor

Kent State University, Bachelors, Marketing. Kent State University at Kent, Masters in Education, Special Education.

View Tutors

Rainier
Certified Tutor

Norfolk State University, Bachelors, Physics.

View Tutors

Patrick
Certified Tutor

LeTourneau University, Bachelors, Electrical Engineering. LeTourneau University, Masters, Electrical Engineering.

All Common Core: 7th Grade Math Resources

7 Diagnostic Tests 110 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in Dallas Fort Worth, GRE Tutors in San Francisco-Bay Area, ISEE Tutors in Chicago, English Tutors in Philadelphia, English Tutors in Seattle, SAT Tutors in Phoenix, English Tutors in San Francisco-Bay Area, Biology Tutors in Philadelphia, SSAT Tutors in Phoenix, Biology Tutors in New York City

Popular Courses & Classes

MCAT Courses & Classes in Phoenix, SAT Courses & Classes in Phoenix, GRE Courses & Classes in Los Angeles, SSAT Courses & Classes in Los Angeles, GRE Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Boston, GMAT Courses & Classes in Phoenix, Spanish Courses & Classes in Seattle, ISEE Courses & Classes in Miami, ACT Courses & Classes in Philadelphia

Popular Test Prep

GRE Test Prep in Los Angeles, GRE Test Prep in San Diego, GRE Test Prep in Chicago, ISEE Test Prep in Dallas Fort Worth, MCAT Test Prep in Phoenix, ACT Test Prep in Chicago, ACT Test Prep in Philadelphia, LSAT Test Prep in Denver, LSAT Test Prep in Atlanta, GMAT Test Prep in New York City

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

Common Core: 7th Grade Math : Know and Use the Formulas for the Area and Circumference of a Circle: CCSS.Math.Content.7.G.B.4

Study concepts, example questions & explanations for Common Core: 7th Grade Math

All Common Core: 7th Grade Math Resources

Example Questions

Example Question #1 : Area Of A Circle

Example Question #1 : Radius

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

Example Question #11 : Know And Use The Formulas For The Area And Circumference Of A Circle: Ccss.Math.Content.7.G.B.4

Example Question #22 : Radius

Example Question #11 : Area Of A Circle

Example Question #12 : Area Of A Circle

Example Question #11 : Radius

Example Question #141 : How To Find The Area Of A Circle

Example Question #13 : Area Of A Circle

All Common Core: 7th Grade Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: