We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Pre-Algebra : Area

Study concepts, example questions & explanations for Pre-Algebra

Create An Account

All Pre-Algebra Resources

11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #54 : Area Of A Circle

Find the area of a circle if the radius is $2\sqrt2$ .

Possible Answers:

$8\pi$

$4\pi$

$6\pi$

$12\pi$

$16\pi$

Correct answer:

$8\pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius into the formula.

Remember when squaring the radius, square both terms. Also recall that when two square roots that have the same base are multiplied together, the square root sign disappears and you are left with the number underneath the square root sign.

$(2\sqrt{2})^2=2^2\cdot \sqrt2\cdot \sqrt2=4\cdot 2$

Therefore the area becomes,

$A=\pi (2\sqrt2)^2 = \pi (4\times 2) = 8\pi$ .

Report an Error

Example Question #55 : Area Of A Circle

Find the area of a circle if the circle has a perimeter of .

Possible Answers:

$18\pi$

$\frac{9}{\pi}$

$6\pi$

$36\pi$

$\frac{6}{\pi}$

Correct answer:

$\frac{9}{\pi}$

Explanation:

The circle's perimeter is the same as the circle's circumference.

Write the circumference formula for the circle.

$C=2\pi r$

Substitute the circumference and solve for the radius.

$6=2\pi r$

$r=\frac{3}{\pi}$

Write the formula for the area of a circle.

$A=\pi r^2$

$A=\pi (\frac{3}{\pi})^2 = \pi (\frac{9}{\pi^2}) =\frac{9}{\pi}$

Report an Error

Example Question #56 : Area Of A Circle

Suppose the circle is inscribed inside a square touching all four sides of the square. The side length of the square is 2. What is the area of the circle?

Possible Answers:

$\frac{\pi}{2}$

$2\pi$

$\sqrt2 \pi$

$\pi$

$4\pi$

Correct answer:

$\pi$

Explanation:

Since the side of the square is 2, the diameter of the circle must also be 2. The radius of the circle is half the diameter, which would be 1.

Write the formula for the area of the circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi r^2 = \pi (1)^2 = \pi$

Report an Error

Example Question #171 : Area

Solve for the area of a circle if the radius is .

Possible Answers:

$4\pi + \pi x^2$

$4\pi x^2$

$4\pi x$

$4\pi^2 x^2$

4+x^2

Correct answer:

$4\pi x^2$

Explanation:

Write the formula to find the area of a circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi (2x)^2 = 4\pi x^2$

Report an Error

Example Question #58 : Area Of A Circle

Find the area of a circle with a diameter of .

Possible Answers:

$\frac{\pi x^2}{4}$

$\pi x^2$

$4\pi x^2$

$\frac{\pi x^2}{2}$

$2\pi x^2$

Correct answer:

$\frac{\pi x^2}{4}$

Explanation:

Write the area of the circle.

$A=\pi r^2$

The radius is half the diameter.

$r= \frac{d}{2} = \frac{x}{2}$

Substitute the radius into the area formula.

Remember that when a fraction is squared, both the numerator and denominator are squared.

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

Report an Error

Example Question #59 : Area Of A Circle

Solve for the area of the circle if the circumference is $16\pi$ .

Possible Answers:

$256\pi$

$96\pi$

$16\pi$

$64\pi$

$8\pi$

Correct answer:

$64\pi$

Explanation:

Write the formula for the circumference of a circle to find the radius.

$C=2\pi r$

$16\pi=2\pi r$

Divide by $2\pi$ on both sides of the equation.

$\frac{16\pi}{2\pi}=\frac{2\pi r}{2\pi}$

$\frac{2\pi \times 8}{2\pi}=\frac{2\pi r}{2\pi}$

Cancel out the $2\pi$ in the numerator and denominator. The radius is:

r=8

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius and find the area.

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

Report an Error

Example Question #55 : Area Of A Circle

Find the area of a circle if the radius is $\sqrt7$ .

Possible Answers:

$49\pi$

$\sqrt{\pi+7}$

$\pi\sqrt7$

$\sqrt{7\pi}$

$7\pi$

Correct answer:

$7\pi$

Explanation:

Write the formula to find the area of a circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi (\sqrt7)^2$

When a square root is squared, the square root is eliminated.

$(\sqrt x)^2 = (\sqrt x)(\sqrt x)=x$

Expand the terms.

$A=\pi (\sqrt7)^2 = \pi (\sqrt7)(\sqrt7) = 7\pi$

Report an Error

Example Question #172 : Area

Solve for the area of a circle with a radius of 9.

Possible Answers:

$18\pi$

$324\pi$

$36\pi$

$27\pi$

$81\pi$

Correct answer:

$81\pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the length of the radius into the equation.

$A=\pi (9)^2$

Expand and simplify.

$A=\pi (9)^2 = \pi (9)(9) = 81\pi$

Report an Error

Example Question #172 : Area

Solve for the area of a circle if the perimeter of the circle is $10\pi$ .

Possible Answers:

$25\pi$

$10\pi$

$2\pi$

$100\pi$

$50\pi$

Correct answer:

$25\pi$

Explanation:

The perimeter is similar to the circle's circumference.

Write the circumference formula.

$C=2\pi r$

Substitute the circumference to find the radius.

$10\pi=2\pi r$

Divide by $2\pi$ on both sides of the equation.

$\frac{10\pi}{2\pi}=\frac{2\pi r}{2\pi}$

r=5

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi r^2 = \pi (5)^2= 25\pi$

Report an Error

Example Question #173 : Area

Determine the area of a circle with a diameter of five.

Possible Answers:

$25\pi$

$\frac{25}{4}\pi$

$\frac{25\pi}{2}$

$12\pi$

$10\pi$

Correct answer:

$\frac{25}{4}\pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Divide the diameter by two to get the radius.

$r=\frac{d}{2} = \frac{5}{2}$

Substitute the radius. Expand the fraction and multiply the numerator by the numerator, and the denominator with the denominator.

$A=\pi (\frac{5}{2})^2 = \pi (\frac{5}{2})(\frac{5}{2}) = \frac{25}{4}\pi$

The area of the circle is: $\frac{25}{4}\pi$

Report an Error

View Pre-Algebra Tutors

Michelle
Certified Tutor

University of Nevada-Las Vegas, Bachelor of Science, Mathematics.

View Pre-Algebra Tutors

Dejuan
Certified Tutor

University of Illinois at Urbana-Champaign, Bachelor of Science, Electrical Engineering.

View Pre-Algebra Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

All Pre-Algebra Resources

11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Algebra Tutors in San Francisco-Bay Area, GRE Tutors in Boston, Statistics Tutors in New York City, Statistics Tutors in San Francisco-Bay Area, Algebra Tutors in Denver, Reading Tutors in Houston, Physics Tutors in Los Angeles, Computer Science Tutors in Phoenix, Chemistry Tutors in Phoenix, SAT Tutors in Miami

Popular Courses & Classes

Spanish Courses & Classes in Washington DC, MCAT Courses & Classes in Denver, ACT Courses & Classes in Atlanta, LSAT Courses & Classes in Boston, ISEE Courses & Classes in Houston, ISEE Courses & Classes in Denver, Spanish Courses & Classes in Chicago, GRE Courses & Classes in Philadelphia, ISEE Courses & Classes in Boston, GMAT Courses & Classes in Miami

Popular Test Prep

SAT Test Prep in Philadelphia, SSAT Test Prep in Los Angeles, MCAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Seattle, ACT Test Prep in Dallas Fort Worth, MCAT Test Prep in Denver, GMAT Test Prep in Denver, ISEE Test Prep in Denver, LSAT Test Prep in Houston, GRE Test Prep in Seattle

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

Pre-Algebra : Area

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #54 : Area Of A Circle

Example Question #55 : Area Of A Circle

Example Question #56 : Area Of A Circle

Example Question #171 : Area

Example Question #58 : Area Of A Circle

Example Question #59 : Area Of A Circle

Example Question #55 : Area Of A Circle

Example Question #172 : Area

Example Question #172 : Area

Example Question #173 : Area

All Pre-Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: